chore: Restore PrivateSentrySDKOnlyTests

[itaybre]

Looks like we have this test file but never added it to the project.
This PR adds it again and updates broken tests due to changes in the code.

#skip-changelog

Closes #6520

[codecov]

❌ 1 Tests Failed:

Tests completed	Failed	Passed	Skipped
4030	1	4029	28

View the top 1 failed test(s) by shortest run time

iOS_SwiftUI_UITests.LaunchUITests::testNoNewTransactionForSecondCallToBody

Stack Traces | 0s run time

.../iOS-SwiftUI/iOS-SwiftUI-UITests/LaunchUITests.swift:37 - Failed to tap "Form Screen" Button: Timed out while evaluating UI query.

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[github-actions]

Performance metrics 🚀

	Plain	With Sentry	Diff
Startup time	1232.24 ms	1258.84 ms	26.59 ms
Size	23.75 KiB	1.00 MiB	1006.01 KiB

Baseline results on branch: main

Startup times

Revision	Plain	With Sentry	Diff
3ec47ae	1229.71 ms	1257.13 ms	27.41 ms
37238de	1236.00 ms	1267.80 ms	31.80 ms
102cf89	1218.31 ms	1239.78 ms	21.47 ms
26f7b17	1218.47 ms	1253.82 ms	35.35 ms
c63e0fe	1230.58 ms	1253.94 ms	23.35 ms
8da82b4	1220.08 ms	1248.24 ms	28.16 ms
f97a070	1218.88 ms	1253.12 ms	34.24 ms
5840d2d	1225.40 ms	1241.47 ms	16.07 ms
2609f7a	1218.17 ms	1241.34 ms	23.17 ms
93c76b0	1236.92 ms	1265.82 ms	28.90 ms

App size

Revision	Plain	With Sentry	Diff
3ec47ae	23.75 KiB	919.91 KiB	896.16 KiB
37238de	23.75 KiB	963.18 KiB	939.43 KiB
102cf89	23.74 KiB	891.02 KiB	867.27 KiB
26f7b17	23.75 KiB	960.93 KiB	937.19 KiB
c63e0fe	23.74 KiB	874.08 KiB	850.33 KiB
8da82b4	23.75 KiB	913.63 KiB	889.88 KiB
f97a070	23.75 KiB	858.68 KiB	834.93 KiB
5840d2d	23.75 KiB	969.24 KiB	945.50 KiB
2609f7a	23.75 KiB	867.04 KiB	843.29 KiB
93c76b0	23.75 KiB	946.69 KiB	922.95 KiB