Does this game feature a time limit?

[MindfulOcean]

When I tried the demo, I found the game took some getting used to. Will I be punished if I take time to learn the ropes and avoid completing the main quest for a while?

[Kargor]

Once you take a "commission"/"quest", there might be a time limit on it. For main quests in particular, you can generally just let them sit there.

A few other things might have time limits as well. For example, once I decided to "marry" Emily, I also learned that she has a special quest that basically needs to be done on one specific day. You can still "marry" her normally at any day, though.
There might be other situations like this, although I only know that one. Other NPCs have special marriage quests as well, though.

[worstcase11]

Some quests happen at a certain time, and if you don't have the neccessary blueprints unlocked till then (especially the cooking set) you can't complete them, but there is not much impact aside from missing a chance to build some friendship points and earn some cash from declining those quests.

The game will send your character off to bed at 3am, if they didn't turn in already, but again there is no punishment just the character being sent home and the game being saved.
That said, if you want to enter a dangerous ruin, the neccessary time will be deducted from what is left of your day (example, if you enter a DM level that that is set to 5 hours clearing time at 7pm, you leave the level at exactly 0am, no matter how long you actually needed to clear it when inside. If the set time is so long that you will exceed the 3am bedtime limit, you can't enter that level anymore on that day and have to try coming back another time.

Daily commissions from the commerce guild always have a time limit, so only pick those you are sure you can complete, ideally within the same day (fridays will have special commissions which can be more challenging but give more rewards as well, as saturday and sunday wont offer daily missions.)

Once your workshop gais some reputation, you can play a minigame at the C-guild every saturday and sunday with very useful rewards- if you go there before 3pm.

Story missions sometimes don't have a time limit, the Bridge to Amber Island mission you get right at the start is such a mission. You can delay it as long as you like, however that will also delay your access to new regions with new resources. (In my opinion it is best to finish the Bridge project, as soon as you have assembled enough materials and the means to build 5 Dee-Dee transports.)

Annual Events usually are time sensitive - in some cases you need to sign up before a deadline and be punctual at the event start to take part in contests. Since event rewards are some of the best in the entire game, make sure not to be disqualified for being late.