This has come up a lot before, including by myself.
I think the bottom line is this…
The remaining attribute does not ever update when a timer is active. In fact I believe that timers don’t even actually count down the time at all but when they are started they work out what time they will finish and then stop at that time.
Lovelace will display the countdown (I assume by working it out) but I find it doesn’t always keep updating if the tab loses focus. Also it only works at all if you do not start the timer again before it has finished. In that case it will just show active and the initial time.
@petro in another post said he looked at the code and one way to get the remaining time is to pause the timer. This will populate the remaining attribute. Not useful for time critical purposes but I can confirm it works as I have spent all day today rewriting all my PIR sensor code using pauses and starts to allow me to have reliable data with sensors that sleep for four minutes after four activations within four minutes (but that is another story).
I hope this is helpful.