Yes, it does.
When reversed, nothing states that the extra-planar creature can't enter, but it explicitly says it can't leave, the very definition of a trap for pests.
The main purpose of the reverse circle is to contain creatures you're summoning so it needs to let them in. Thanks to Mark Wells for the heads up.
Your extra-planar flypaper, besides the 1 hour short duration and the fact that there are easy to see glowing runes on the floor, is functional. But looking at these points make it not the best choice for a trap.
It's not easy, but you can escape quickly if you have the right tools.
The phrase "a creature inside the cage can't leave it by nonmagical means" doesn't mean you can just turn yourself into a mouse/gas/etc and move out. Walking or flying are mundane movement, even if it was magic that gave you a fly speed or changed your physical size. Your method of leaving must itself be magical, which means it's basically going to be teleportation or planar travel, so you're up against the save. That excludes the "easy" methods of gaseous form or wild shape, polymorph, etc. as escape routes.
Sure, you can spam misty step to get out sooner or later, but that does require you to know the spell (and have it prepared, if that's a thing for you), and potentially burn a bunch of spell slots and waste a bunch of turns, just to escape from one spell. I don't call that "easy". Simple, if you have the proper tools at hand, but costly. (I'm making that distinction in the same sense that walking up a mountain is simple, but not easy.) There are a number of "save or suck" effects that give you another try at the save every turn, but unlike forcecage most of them don't cost you spell slots every time you try. But yes, trapping a powerful spellcaster inside a forcecage is probably not your best use of the spell.
Antimagic field is a sure-fire escape method, from inside or outside, but escaping a 7th level spell by casting a very specific 8th level spell is a very high cost indeed. You only get one 8th level spell per day, ever, so burning that merely to escape a forcecage is a hefty price -- and again, you have to have that AMF spell prepared already, or available through some other method, like a spell scroll.
Disintegrate seems like it would work in this case, whether the caster is inside or not. A forcecage is specifically a "prison composed of magical force", and disintegrate can target a "creation of magical force", so it's a valid target, and it "automatically disintegrates" a ten-foot cube out of a creation of force that's Large or larger. I can't see any reason a disintegrate spell would not work to open a hole in a forcecage. That said, again, you're defeating a 7th level spell with a specific 6th level spell, of which you only ever get 2 per day. While it's not as uncommon as an antimagic field, it's still a significant cost that the party may not have access to. There are many such pairs of spells where one can specifically counter another.
Best Answer
Yes. Tree stride and transport via plants do not incur the charisma save to escape from a force cage
Both tree stride and transport via plants provide a location shifting effect, but do not state they are teleporting the caster. Spells that teleport the caster state they do so in the effect text.
The drawback is the plant spells are dependent on the presence of a tree or large inanimate plant inside the force cage's area. Clever use of a tree or mass of plants if they are available.
Teleporting spells
In contrast, spells that teleport the caster state this, e.g. " you teleport..." "You and up to five willing creatures within 5 feet of you instantly teleport..." The following spells all indicate they are teleporting the caster and are subject to the charisma saving throw effect:
Availability
An import difference here is that the spells that afford magical movement that isn't teleportation are dependent on the presence of a suitable trees or plants whereas the direct teleportation spells are always available to the caster.