OK to connect boards perpendicularly like this?
You don't mention board type etc. here is some feedback:

You have to be aware of the shear stresses which can cause de-lamination of the copper traces from the board underneath.  You do have a huge lever arm to develop high forces.  This could be reinforced with vias in those fingers, if you have vias available that is ....

However, this sort of approach is best done in a pierce and blank assembly line (probably with single sided copper) and phenolic boards.  The reason for that is that it is possible to have the stamping operation get you nicely square corners on the cutting die.

In a past project, this is what we did.  Do keep in mind that cost was critical, we were counting 1/10th of a cent for resistors as being too much whereas labor cost was not an issue.  The device itself was potted for protection/longevity and safety.



Rather than have individual "pins" as you drew we had slots.  We used the precision of the stamping tool along with a precise jig for soldering (by hand).

Also, there were three boards that interlocked and self supported.  So that once assembled (without solder ) they were very robust.  It took some work to get right, but putting a connector in there was a non-starter because of the extreme cost pressures.

here is a quick sketch of 3 intersecting boards and slots.



Here is a picture from a development board that I still had kicking around.  These boards where done in FR-4 to allow us to study thermal and mechanical effects before moving to the expensive pierce and blank dies and phenolic boards (I  didn't keep any of those unfortunately), other wise you'd see square corners and tighter tolerances.  This was also used to study solder wetting and the assembly process tolerances and ease of manufacturing.



This board is quite beat-up from being at the bottom of a drawer for many years.

So yes it is doable, to the tune of 100Kunits per month.