I have 2 spare R7000 shifters which I used on my rim brake equipped road bike. I've upgraded to Ultegra some time ago. I also have a Tiagra gravel bike with mechanical disc brakes that uses Tiagra shifters. Will I be able to equip my R7000 on that gravel bike? I.e. are there any compatibility issues possible or is it ok so long as both shifters are mechanical?
The R7000 shifters are 11-speed shifters and require 11-speed pull ratio rear deraileur and 11-speed cassette.
I'm not sure if your Tiagra is 4700 or earlier. If it's 4700 then despite being a 10-speed system it uses the 11-speed derailleur cable pull ratio, so it will work with 11-speed shifters provided that you use 11-speed cassette.
If the Tiagra is earlier than 4700, then you need to not only use 11-speed cassette but also switch to an 11-speed rear derailleur.
Also do note 11-speed "road" cassettes are not compatible with regular width freehubs. They require special 11-speed "road" hubs. You can avoid this compatibility problem by using an 11-speed "MTB" cassette (one that has big enough big sprocket) that overhangs the hub flange and thus is compatible with old width freehubs -- but do note some "road" derailleurs may lack the big sprocket support or the capacity needed by such "MTB" cassettes. Note also that some 10-speed road/gravel bikes are designed with compatibility in mind and have 11-speed compatible hub with a spacer to allow using 10-speed cassette.
The braking cable pull ratio is very similar in all STI brifters. If your mechanical disc brakes work with one STI brifter, they work with all STI brifters. So for example long pull mechanical disc brakes (having similar pull ratio than V brakes) will never work with an STI brifter.