I noticed that the timing of the strength save on entangle is strange. The save to escape triggers at end of turn which would be fine but that's also when the save to see if you get stuck takes place. The result is if you pass to escape you must then pass the same save again or stay restrained.
forcing the save to be passed twice in a row doesn't seem to be the intention of the spell and is very powerful.
With Entangle, if a creature fails their initial saving throw, they stay restrained until the spell ends. They do not get a free saving throw every turn to see if you are no longer restrained (some spells do this, but not Entangle). They can choose to use their Action to try and free themselves and on a successful save, they can move (but can't also take an action, since they already used their action to free themselves). But they can also choose to not try and free themselves and instead use their action to Attack (at Disadvantage) or some other Action.
I see this working as designed. Unless you are saying they are making two separate saving throws per turn? I have not seen this with Entangle.
When entangled there was not an option to attempt a saving throw as an action, instead it happened at the end of turn. meaning if you passed the saving throw you wouldn't have the ability to move before you had to make another save. even when using your action to do something else it would still proc a saving throw at end of turn to try and escape and if that passed would proc another saving throw for ending the turn in the effect.
So yes with entangle it was making two saving throws per turn once you have been restrained once.
Can you share which battle you are fighting where the enemy NPC casts Entangle on the party? I have not seen this; only the party casing Entangle on the enemy NPCs.
Early on in the second campaign the party was ambushed on the road by a group of 4 dryad that cast entangle. This can also be observed by casting entangle on any enemy group and watching the saves. I haven't tried casting it on my own party yet but that could work to check as well.
So I did go back into game and cast entangle on my barbarian to confirm that the save is occuring at end of turn instead of as an action and that if you failed previously you will need to pass two saves at the end of the same turn to break out.