In practical terms, knowing where you are in the process can give you back control, you are in the driving seat. You have a 3 month deadline to lodge your claim online, counting from when the 'event' happened eg discrimination. It is rare that the Court will extend that deadline.
You have little to lose by lodging your claim, as Tribunal is fee-free. Entering into ACAS Early conciliation is helpful because it forces your employer to reveal their intentions as to whether they are willing to enter into a Settlement Agreement to avoid Tribunal. This depends on whether your Claim is strong.
The key thing is, time will become the driver, due to court deadlines. If they have been using delay tactics to date, they won't be able to keep doing that. Meanwhile, you can pull out right up until the day of Tribunal, without necessarily incurring significant cost You don't need to make any decision for a while yet
I would advise you to seek new employment as soon as possible. It will be good for your morale to focus on the future and it complies with the Court's expectation that you as the Claimant are mitigating Loss. So it's a win-win.
If your contract is for fully paid sick leave, then stay on sick leave. IMO once this type of situation happens it is very difficult to turn back the clock, repair fractured trust and return to work. Better to leave (once you get a new job) and start afresh. Use your sick leave to rebuild your emotional strength, be proud of yourself for surviving thus far, and remember your future life awaits, with rich experiences gained. It is a very challenging time, so give yourself permission to have a few wobbles. Main thing keep focus on the end goal, which depends on what you want to achieve.