Advantages/disadvantages of having AirPort/Time Capsule between ISP router and LAN devices?
My reasoning has been that I don't really trust the ISP/router
manufacturer completely and that I would be safer with my devices
behind the Apple Router.

If you don't trust the ISP router (I agree with this), use your own router.  Also, your Time Capsule is dated as you guessed so I would recommend replacing it with something newer and more modern.
What you will need is the following:

Put your Technicolor Router in Bridge Mode
New router/wireless access point(s)

Bridge Mode
This mode &quot;bridges&quot; two networks together, in this case, your network (which you will create with your router) and the ISP's network.  This will require you to have your own router because it turns of router/firewall functionality of the Technicolor (including NAT).

It seems the ISP router can't be set in Bridge mode, and I think the
ISP doesn't prefer that as they sometimes access it for diagnostics,
etc.

It can, it's just a feature they would rather you not use (you take them out of the loop for your internal networking).  As for diagnostics, they don't need it in firewall mode to service your modem - they work with it by addressing the MAC address, not the IP.
New Router
You could use the Time Capsule, but (IMO) you should get a new router with newer features, security capabilities and Wi-Fi protocols.  The Time Capsule doesn't give you any benefit other than having an all in one solution for your router and Time Machine backups.  You can still turn off the router/firewall function and just use it for network based backups if you like.
Which router?  Pretty much any router you buy off-the-shelf will work fine.
My recommendation
I would use a pfSense router (open source and free) that's installed on a cheap PC.  There's an excellent YouTube video on this very build which you can follow.   Then for Wi-Fi, I went with a Ubiquiti access point.
Is this overkill for a home? Yes.
This is a more &quot;enterprise&quot; grade setup than a consumer grade setup you would get with a router purchased from your local electronics retailer.  What I have found is that this is much more stable and reliable.  The off-the-shelf stuff (like Netgear, Linksys, Asus etc.) would die within 18 months.  I've been running my pfSense for 3 years now with no issues.  Updates are about as easy as updating your Mac.