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	351.96 ms	384.72 ms	32.76 ms
Size	1.58 MiB	2.10 MiB	532.31 KiB

Baseline results on branch: main

Startup times

Revision	Plain	With Sentry	Diff
ee747ae	405.43 ms	485.70 ms	80.28 ms
ee747ae	357.79 ms	421.84 ms	64.05 ms
85d7417	347.21 ms	394.35 ms	47.15 ms
b750b96	408.98 ms	480.32 ms	71.34 ms
ee747ae	358.21 ms	389.41 ms	31.20 ms
ee747ae	415.92 ms	470.15 ms	54.23 ms
b750b96	421.25 ms	444.09 ms	22.84 ms
c8125f3	383.82 ms	441.66 ms	57.84 ms
ee747ae	554.98 ms	611.50 ms	56.52 ms
7314dbe	437.83 ms	505.64 ms	67.81 ms

App size

Revision	Plain	With Sentry	Diff
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
85d7417	1.58 MiB	2.10 MiB	533.44 KiB
b750b96	1.58 MiB	2.10 MiB	533.19 KiB
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
b750b96	1.58 MiB	2.10 MiB	533.20 KiB
c8125f3	1.58 MiB	2.10 MiB	532.32 KiB
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
7314dbe	1.58 MiB	2.10 MiB	533.45 KiB

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

Startup times

Revision	Plain	With Sentry	Diff
6490d25	412.75 ms	490.53 ms	77.78 ms

App size

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