Rework timer delays

[amelchio]

Description:

@pvizeli noticed that #16598 ignores a quite important special case.

I have now reworked the timer so resetting – and startup – are no longer special cases (the first commit). We simply always delay until the next second rolls around.

The second commit adds back the well-known error message of an unsynchronized timer even though the reset is not explicit anymore.

Checklist:

• The code change is tested and works locally.
• Local tests pass with tox.

If the code does not interact with devices:

• Tests have been added to verify that the new code works.