There are no softlocks or missables. There were reports of issues when changing rooms before certain animations were complete, but these may have been patched. Chapter 10 (especially) and Shattered Quadrant are by far the longest. Some secrets and monoliths cannot be accessed until you unlock a mechanic later in the game that persists between chapters once set.
To get back to the rest of the level upon revisiting chapter 9, move one of the shards to layer 8.
In chapter 6, there is one secret that is more difficult to get if you don't get it along the way. See this topic for some tips if you're returning for it.
You can start Shattered Quadrant when you unlock it and make some progress, but to be able to get to all areas/items and finish it, you will have to find all the Monoliths in the regular levels. The game highlights which tickets you have never visited, but there is significant backtracking and there are 43 total tickets, so I recommend keeping track of your progress and what you find in each area.
You can change to the classic sound effects in the options, if you miss them from the original games.
Guide to everything except Shattered Quadrant (postgame): Loading Steam guide...
Shattered Quadrant guide:
Loading Steam guide...
Flowchart-style maps of all levels (likely the only times you'll really want to make or look up a map are chapter 8 and portions of SQ, as opposed to just keeping a few notes and in some chapters tracking combinations):
Loading Steam guide...
These guides are the best for if you play along on your own and get stuck. Other guides are also available. Changes have been made from the original versions of the games, so guides that predate the Steam release may not fully apply.
Enjoy your exploration of the Submachine!