is there a time limit in each playthrough?

[OceanPink]

As title

[CaoLex]

Not really.
To be more specific, there is time limit for the "true ending", but it's ending also nukes your game, making it unplayable anymore (if devs hasn't changed anything) for the plot reasons.
If you don't achive this ending thought then you can play however long you want.
The game difficulty doesn't really scale with time (aside of the initial temporaly "defence from bad events") in any significant manner, it scales from your sect renown and bad relationship with other sects.
And I don't recommend going for a "true ending" anyway.
There are some non-repeatable events that have time limits, what give you some advantages if you manage to finish them, but you can just as well ignore them.
Even the beast on your sect map getting awakening isn't really problem for a very long time unless you deliberatly provoke it while being too weak do defend.
If you want to play slowly, then your concern is being strong enough to repell Flood Dragon (and later Phoenix) to not have need to pretty much rebuild your sect but keep low enogh renown to not trigers constant raids from other sects uncles. You will serve as a "retirement policy" for other sect weaklings either way, but they are more or less free loot instead of treat.

[Perro Grande]

There is a tribulation option that makes attacks stronger as time passes, which eventually will lead to the attacks being so strong you cannot win, but that would easily take over 1000 ingame days to get to, probably over 2000 depending on how strong you can get your sect. You would probably get bored of the game before you hit the theoretical limit of when the bonuses from that option surpass anything you can do.