ref(core): Replace RootChecker with MIT licensed version

[lcian]

Close #4687

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Performance metrics 🚀

	Plain	With Sentry	Diff
Startup time	423.13 ms	477.73 ms	54.61 ms
Size	1.58 MiB	2.10 MiB	533.21 KiB

Baseline results on branch: main

Startup times

Revision	Plain	With Sentry	Diff
ee747ae	382.73 ms	435.41 ms	52.68 ms
ee747ae	415.92 ms	470.15 ms	54.23 ms
ee747ae	400.46 ms	423.61 ms	23.15 ms
ee747ae	554.98 ms	611.50 ms	56.52 ms
ee747ae	358.21 ms	389.41 ms	31.20 ms
3699cd5	423.60 ms	495.52 ms	71.92 ms
85d7417	347.21 ms	394.35 ms	47.15 ms
7314dbe	437.83 ms	505.64 ms	67.81 ms
ee747ae	357.79 ms	421.84 ms	64.05 ms
ee747ae	374.71 ms	455.18 ms	80.47 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
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
3699cd5	1.58 MiB	2.10 MiB	533.45 KiB
85d7417	1.58 MiB	2.10 MiB	533.44 KiB
7314dbe	1.58 MiB	2.10 MiB	533.45 KiB
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB

Previous results on branch: lcian/ref-root

Startup times

Revision	Plain	With Sentry	Diff
ef493cf	388.90 ms	465.98 ms	77.08 ms
b8e49e0	383.83 ms	418.57 ms	34.74 ms

App size

Revision	Plain	With Sentry	Diff
ef493cf	1.58 MiB	2.10 MiB	533.47 KiB
b8e49e0	1.58 MiB	2.10 MiB	533.21 KiB