As an example, I can currently get Zoe to unlock the roof access as the first room I unlock in the game. As soon as this is unlocked, room 101 is also unlocked (even though it should only be unlocked by the Celeste task to meet her in her office). A second example, I can buy the room upgrade from Scruffy prior to Celeste calling me to her office. Once the room is upgraded, Celeste still eventually tells me to clean it, but the game won't let me (presumably the mold was removed by Scruffy during the upgrade, so either cleaning is an irrelevant task, or I completely lost any benefits from that branch because I didn't follow the unknown game-script order).
Also, while I can understand some of your programmatic reasons for many of the "accept task" commands, I tend to find them more problematic as a player than anything. Once again back to the Celeste stop-by-my-office task, I go to the lounge and she tells me to meet her in her office at nine (repeating my comment that this should say 21 instead). Everything about this reads as a command (i.e. a task that is assigned/accepted whether we want it or not without any input needed from us). Then, depending on whether or not 101 is unlocked (it was for me because I had already taken lotion to the roof, but may not be if you haven't done that task or typed "accept" for the office), the player waits until 21 and either can't figure out why he can't get access to the office to keep his meeting, or he goes to the meeting and can't get Celeste to speak to him at all because her event hasn't been activated. Presumably nothing is broken. The player can go on a later day and have the task presented to him again and again until eventually he "accepts". But this is vague at best, and of absolutely no help to someone sitting frustrated at 21 trying to finish a task he considers active.
The above does reiterate one of the potential benefits of a task journal. If the player could type "active tasks", or some other command, and see what tasks are currently running, this would help the above situation. While it still wouldn't be ideal, at least the player would have the ability to see that, hey, meeting her in her office is not currently running. This helps the player decide to maybe stop trying to talk to her at 21 and also gives a clue that maybe next time she says to meet her in her office that maybe the task must be accepted to continue.
If, for programmatic reasons, you do really find a need to have the player accept all of these tasks, you may want to consider contriving an object for each one. The Gem/lotion event is a good example. Whether or not it is clear to the player that he needs to "accept task" versus just automatically being assigned the task, he needs the lotion to succeed with the task. You've made taking the lotion an inherent accepting of the task. For going to the office, you could contrive something like, "You need to dock your badge with my tablet for me to unlock the first floor for you." Docking the badge could be a frequent requirement as a means of accepting tasks. Or, just as Zoe apparently had the ability to change our area access, the task could be not worth Celeste's time. She could have said, "ask Zoe to unlock level 1". Asking Zoe could start the task. As another option, Celeste holds up a new uniform/patch/medal/whatever and tells us that employee dress displays the rank of the wearer. With additional access comes a higher rank. The player needs to take and wear the new item (and thereby accepts the task). The point being, if the player needs to do something, even if what they need to do is considered a puzzle for them to solve, they certainly need to be told that something must be done.
As a random aside, it still has a bit of an odd feel that many of the Celeste tasks only happen if/when we stumble across her at the appropriate place and time. It works fine to match how the rest of the game seems to play, but from an immersion/logic point of view doesn't so much fit. If a boss wants an employee to do a job, or come to a meeting at a specific hour, they are going to hunt that employee down and make it happen (not to mention it wouldn't likely be an optional task at that point). I realize that part of the game setup is to imply that the player needs to put in normal work hours and secretly require that he do exactly the opposite of that (making him constantly skip work to be available to find any of the events to progress the story). So doing things like, Celeste wants the player to meet with her at 21, but she'll only tell him about that if he walks into the lounge at exactly 14 is both perfectly expected/reasonable/required to match the rest of the game, and totally nonsensical from a reality viewpoint. As I said, just an aside that seemed worthy of being mentioned, even if completely ignored in the end.