Hi
@Alex321 , just scanned your posts and not too sure about exactly what's happening but in your OP you mentioned you were having problems changing up to the large front chainring. I recently had a very similar problem and went through the same thought processes as you ie is it the shifter, cable, etc and was getting around to thinking I needed a new shifter when I stumbled across a really easy fix which which worked for me (I've got Ultegra R8000 shifters) on youtube:
View: https://www.youtube.com/watch?v=-mCwvDtRw8U&list=PLLDtighiMfmBeeJaSQlUZla1EPOZ2yrOt&index=3
Basically when you push the the large lever inwards it also pushes the smaller lever and both need to move inwards exactly in time, otherwise the internal ratchet system doesn't work properly ( I was getting some horrible crunching noises). If there is a gap between the two levers they don't move in time and so the ratchet doesn't work properly, the video explains this better. In my case I added a 2mm thick piece of plastic between the levers as shown in the video and it cured my problem completely. I've also applied the same fix to the right shifter for the rear mech and it has improved the shifting there as well!
I see you've already been to your LBS and you've ordered a new shifter but thought I'd post this anyway as it's really quick and easy to try, if it works you might be able to return the new shifter and save yourself a bunch of money!