Welcome Dennis,
I would recommend reviewing the automation triggers and conditions in HASS and evaluating your current events against them. You may find that what drove you to choose counters and timer devices in HS can be done a different way. HASS supports variables in automations, loops, and some other things not supported in HS that allow for multiple HS events to be collapsed into one HASS automation.
It does appear that HASS is less robust around keeping states over a reboot than HS. Here is a thread on making timers survive a reboot Restore active/paused timers after a restart - Share your Projects! - Home Assistant Community (home-assistant.io) that may be useful.
I’m in the early stages of evaluating my HS event logic using the same logic. I’m compiling a comparison of HASS triggers and conditions to HS triggers and conditions and working on documenting automation patterns so I can apply them to my HS event conversions.
Slow and painful work, but I’d rather not have to redo things once I put them in HASS.