Testing: use synctest throughout

[findleyr]

We have several tests that rely on timing, and have been meaning to replace this with uses of synctest. This issue tracks that work.

(see any usage of the time package in test files)

[jba]

Don't we need the module to be on Go 1.24?

Can we bump it now that 1.25 is out?

[findleyr]

@jba we can just move the tests that rely on timing to a build-tagged file.