Are controllers aware of TCAS RA taking place?
ATC was and is still generally not aware of RAs before being informed by the pilot
In general ATC is not aware of any RA occurring in aircraft, and is neither aware of the RA content. The crew informs ATC using a phraseology described in ICAO Doc 4444 PANS-ATM, Chapter 12, Para 12.3.1.2:

When the RA occurs, and the crew must deviate from ATC instructions, they inform ATC with &quot;TCAS RA&quot; when possible.
If an ATC instruction is received, which contradicts a current RA, they inform ATC with &quot;Unable, TCAS RA&quot;.
The crew then informs ATC when the RA has ended, with &quot;Clear of conflict, returning to (the ATC clearance)&quot;, and &quot;resumed&quot; when done.

See instructions to ATC and RTF Phraseology associated with TCAS RAs.
Pilot and ATCO obligations, impact of RAs on responsibilities
RA always takes precedence on ATC and must be followed by the crew (exceptions are investigated). This is because even if the crew has the intruder in sight and another safe maneuver might be executed as well, there is no certainty the visible aircraft is the conflicting one, or is the only conflicting one.
When informed, ATC doesn't provide further instructions to this aircraft before receiving the &quot;clear of conflict&quot; confirmation.
Two issues should not be overlooked:

According to existing regulations, a controller is not relieved from providing a guidance to pilots until informed by the pilot of a RA conflict (&quot;unable TCAS RA&quot; -- a pilot doesn't have to report RAs not preventing to comply with received ATC clearances). Therefore the (legal) responsibilities and obligations of the controller are unclear in the period between the display of the down-linked RA, which can be delayed by technical limits, and the actual report by the pilot which is not instantaneous.

Not all RAs are relevant to ATC, only those which pertain to collision avoidance or conflict with ATC clearances, therefore some filtering must be done either prior to download, or after reception to eliminate &quot;Monitor Vertical Speed&quot;, &quot;Maintain Vertical Speed&quot;, etc. This filtering may be imperfect and can lead to RA not displayed.


Last but not least, the current view of the controllers federation:

IFATCA is opposed to down linking of any advisories generated by ACAS.
If down linking of ACAS Resolution Advisories becomes mandated, then
IFATCA can only accept this provided that the following criteria are
met:

Clear and unambiguous controller legal responsibilities;
Downlink without delay;
ATC system to be able to receive, process and display the down link to the appropriate control positions;
Compatibility with all ground based safety nets;
Nuisance and false alerts must be kept to an absolute minimum;
ACAS should only be considered as a ‘safety net’.


RA downlink decisions and implementation progress
Due to the responsibility and limitations issues, the adoption of RA display at controller working position is variable among countries, in spite of technical studies confirming the interest (detailed further down), and modern ATC systems being able to receive and manage downlinked RA. Current status for some countries (source):

USA and UK and France don't use it (UK CAA clearly forbids any use).
Czech Republic and Hungary have tested the technology early and use it.
Luxembourg is conducting studies for using it.

Where it is used, the RA data is only for information, and doesn't change ATCO responsibility for collision avoidance, e.g. for Hungary the regulation has been complemented (source):

The TCAS RA Downlink shall be ignored from an operative point of view.
In  other words, it is only for situational awareness and informative
purposes, and the controller shall not consider RA Downlink when
issuing a new  clearance.

UK CAA forbids ANSP to use RA downlink (ibid):

There are currently no ICAO, European or UK pilot procedures, ATC
procedures or legal responsibilities for the use of ACAS RA Downlink.
However, this subject is under consideration by Eurocontrol.
There is no assurance as to the integrity of the RA downlink and
absent or false downlink data could be a possibility.
A downlinked RA without adequate discrimination may lead the ATCO to
inappropriately cease the provision of ATC instructions. However,
under current ICAO procedures, the controller will continue to provide
ATC instructions during RA events that do not deviate from the
clearance or instruction unless such a clearance is at variance with
the RA, at which point the pilot will report ‘UNABLE, TCAS RA’.

Studies conducted to include ACAS RAs in ground-based safety nets
There has been several accidents involving RAs not followed by crews, among them a tragical collision over Switzerland (2002 Überlingen) where the risk was not spotted in time by controllers due to a calamitous chain of events. RAs were issued by both TCAS, one pilot followed its RA, the other followed ATC urgent descent instruction against RA. The BFU report noted &quot;an automatic downlink, integrated in the TCAS equipment, carrying information about issued RA’s to the respective ATC units has not been activated yet&quot; and has recommended to allow RA downlink to inform ATCOs:

To enhance the performance of ACAS
ICAO should initiate the development of down-linking RAs to ATC, using
such technologies as SSR Mode S and Automatic Dependent Surveillance -
Broadcast (ADS-B)

Studies on the feasibility and operational benefits of RA downlink have been conducted in the USA, in France (1994), and in Japan and lately from 2003 to 2007, with the FARADS project which concluded possible short-term downlink solutions would be useful:

With Mode-S RA reports, the controller will be aware about the RAs in
95% of the cases within 9 seconds of their occurrence. Thus, the
downlink of RA information was found to be sufficiently timely to
allow for a significant increase in the controller’s awareness of the
RA encounter.

In the course of this project, RADE-1 and RADE-2 experiments had taken place at Brétigny (France), and concluded in RA downlink benefiting to ATC, without creating a cognitive tunneling around the RA. it also indicated RA downlink could not be deployed without being included in existing ground-based safety nets.
ATC uses ground-based safety nets, which purposes are similar to aircraft ACAS and GPWS, e.g.

Short Term Conflict Alert (STCA): operational since around 2013. An alert in STCA is supposed to take place about 30s prior to a TCAS RA, however this is more complex, and the RA may happens before the STCA alert.

Area Proximity Warning (APW), Minimum Safe Altitude Warning (MSAW) or Approach Path Monitor (APM), all operational since around 2016



RADE-2 experiment showing labels with RA data on first line (source)
Eurocontrol project PASS studied the inclusion of ACAS RA into STCA, and more generally the mutual compatibility and interaction of both systems. In the final report (2010):

An optional real-time experiment with both controllers and pilots
in-the-loop was planned to complement the findings of Phase 1 and to
help define operational requirements supporting an overall operational
concept for joint  STCA/TCAS operations. This optional work was
however not launched due to lack of funding.

The work done concluded the interaction between STCA and ACAS should be considered by ANSP. A few early adopters (Czech Republic, Hungary, Japan, Luxembourg) are experimenting, to answer the question, yes the type of RA is displayed, and whether the aircraft is advised to climb or descend, as visible on the picture above. This is the current status, and obviously everybody is waiting for ICAO (representative of all countries) clarification on the topic.