Remove ApiStatus.Experimental annotations from check-in API

[lcian]

Removes @ApiStatus.Experimental from the whole Check-in API.
Keeps @ApiStatus.Internal where present.

Close #4673

[github-actions]

Performance metrics 🚀

	Plain	With Sentry	Diff
Startup time	383.82 ms	419.78 ms	35.96 ms
Size	1.58 MiB	2.10 MiB	532.96 KiB

Baseline results on branch: main

Startup times

Revision	Plain	With Sentry	Diff
c8125f3	383.82 ms	441.66 ms	57.84 ms
85d7417	347.21 ms	394.35 ms	47.15 ms
ce0a49e	532.00 ms	609.96 ms	77.96 ms
1df7eb6	397.04 ms	429.64 ms	32.60 ms
7314dbe	437.83 ms	505.64 ms	67.81 ms
ee747ae	554.98 ms	611.50 ms	56.52 ms
b750b96	421.25 ms	444.09 ms	22.84 ms
ee747ae	382.73 ms	435.41 ms	52.68 ms
ee747ae	358.21 ms	389.41 ms	31.20 ms
674d437	355.28 ms	504.18 ms	148.90 ms

App size

Revision	Plain	With Sentry	Diff
c8125f3	1.58 MiB	2.10 MiB	532.32 KiB
85d7417	1.58 MiB	2.10 MiB	533.44 KiB
ce0a49e	1.58 MiB	2.10 MiB	532.94 KiB
1df7eb6	1.58 MiB	2.10 MiB	532.97 KiB
7314dbe	1.58 MiB	2.10 MiB	533.45 KiB
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
b750b96	1.58 MiB	2.10 MiB	533.20 KiB
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
674d437	1.58 MiB	2.10 MiB	530.94 KiB

Previous results on branch: lcian/checkin-api-experimental

Startup times

Revision	Plain	With Sentry	Diff
1a52a54	358.50 ms	408.76 ms	50.26 ms
6490d25	412.75 ms	490.53 ms	77.78 ms

App size

Revision	Plain	With Sentry	Diff
1a52a54	1.58 MiB	2.10 MiB	532.96 KiB
6490d25	1.58 MiB	2.10 MiB	532.31 KiB

[adinauer]

LGTM