TYPO3 Core

Some additional information might be helpful:

While using the TSOB, the root page (containing the templates) will show a template selector dropdown.
But any other subpage will show "foo" in the TSOB, although "bar" is the right value.

For friends of copy&paste I'll write the TypoScript again:

Template 1 (hidden)

page = PAGE
page.10 = TEXT
page.10.value = foo

Template 2

page = PAGE
page.10 = TEXT
page.10.value = bar

Moreover you might set the root template values on the "Optios" tab (Clear Constants/Setup and check Rootlevel).

Switching the order (sorting) of the templates, with Template 2 on top and Template 1 below, will show the right values in the TSOB.

Patch set 2 for branch master of project Packages/TYPO3.CMS has been pushed to the review server.
It is available at https://review.typo3.org/c/Packages/TYPO3.CMS/+/63516

Patch set 3 for branch main of project Packages/TYPO3.CMS has been pushed to the review server.
It is available at https://review.typo3.org/c/Packages/TYPO3.CMS/+/63516

Patch set 4 for branch main of project Packages/TYPO3.CMS has been pushed to the review server.
It is available at https://review.typo3.org/c/Packages/TYPO3.CMS/+/63516

Patch set 5 for branch main of project Packages/TYPO3.CMS has been pushed to the review server.
It is available at https://review.typo3.org/c/Packages/TYPO3.CMS/+/63516

Patch set 1 for branch 11.5 of project Packages/TYPO3.CMS has been pushed to the review server.
It is available at https://review.typo3.org/c/Packages/TYPO3.CMS/+/72978