gh-37988: CI Build&Test: Replace use of `sage -t --new`
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Fixes #37985.
We also turn on `--long --format github` for this run, so that
annotations are shown in the "Files changed" tab.
(Previously, only the annotations from the full testsuite run were
shown, out of the concern of duplicating the numerous doctest style
warnings. But these warnings have been much reduced, and the last two
warnings are fixed in #38029.)
Example run: https://github.com/sagemath/sage/actions/runs/9198070834/jo
b/25299950120?pr=37988
### :memo: Checklist
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preview.
### :hourglass: Dependencies
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- Depends on #37926 (merged here)
URL: https://github.com/sagemath/sage/pull/37988
Reported by: Matthias Köppe
Reviewer(s): Kwankyu Lee, Matthias Köppe
