ImGui: Make input recording frame count thread-safe

[TheTechnician27]

Description of Changes

Make the communication between the EE (input recording) and the GS (displaying the frame count via ImGui) thread-safe. Additionally fixes a bug where the frame count was +1 what it should actually be. See #10793, which this is a follow-up to. (This fixes a small bug from that as well.)

Rationale behind Changes

Good to have the correct value displayed (previously we would run into an issue where we would say that we're on a frame that doesn't exist yet; for example, if we'd written 580 frames to an input recording and were actively recording, we'd be on frame 581). And make the code operate in a way that's not subject to a potential race condition.

Suggested Testing Steps

Test input recording to make sure 1) the correct value is displayed and 2) nothing is broken.

Fixes

• Definitely fixes [BUG]: Total input counter is not updated upon loading state (input recording) #8128
• Potentially interacts with [BUG]: TAS save state undo issue. #11454

[kage2051]

It does not fix the determinism issues in some games though. I did a test with Zombie Zone, which seems to have inconsistent RNG between playbacks.

[TheLastRar]

It does not fix the determinism issues in some games though. I did a test with Zombie Zone, which seems to have inconsistent RNG between playbacks.

So you have MTVU enabled or disabled?

[F0bes]

Note that this PR is not rebased on top of #12183

[kage2051]

So you have MTVU enabled or disabled?

MTVU disabled, Optimal Frame Pacing and CDVD Precaching enabled, everything else is at default setting.

[TheTechnician27]

It does not fix the determinism issues in some games though.

Please note that this PR in no way intends to (or in all likelihood does) fix any problems with determinism; this is simply about the way that ImGui displays the current frame count.