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I know the assassin vine (from Tomb of Annihilation) can only constrict 1 creature but does it entangle only 1 as well?

The assassin vine can entangle as many creatures as are in the area.

When the assassin vine takes its Entangling Vines action "a creature in that area when the effect begins must succeed on a DC 13 Strength." The plain-English reading of this effect is that each creature goes through the "am I in the area (Y/N)? If yes, make save" evaluation.

It'll be okay. They're really slow.

The entangle ability description points toward one creature at a time being restrained.

The effect ends after 1 minute or when the assassin vine dies or uses
Entangling Vines again.

Multiple creatures can be subject to the difficult terrain problem, but the decision to use "a" instead of "any" and the last sentence of the description using "again" points to one creature at a time being restrained. The vine would need to try again to restrain another creature.

Entangling Vines

The assassin vine can animate normal vines and roots on the ground in a 15-foot square within 30 feet of it. These plants turn the ground in that area into difficult terrain. A creature in that area when the effect begins must succeed on a DC 13 Strength saving throw or be restrained by entangling vines and roots. A creature restrained by the plants can use its action to make a DC 13 Strength (Athletics) check, freeing itself on a successful check. The effect ends after 1 minute or when the assassin vine dies or uses Entangling Vines again.

Being restrained ends under one of three conditions.

1. It dies




2. 1 minute passes



3. 
   

   when the assassin vine uses the entangling vines ability again.

   
   
   

   There are some other monsters, like a T Rex, that can restrain a creature with a successful bite / grapple, but the restriction on that is that it can only restrain one at a time.

   
   

If the target is a Medium or smaller creature, it is grappled (escape
DC 17). Until this grapple ends, the arget is restrained, and the
tyrannosaurus can’t bite another target.

A roper, on the other hand, can handle multiple roped/grappled creatures at a time (up to six).

Grasping Tendrils. The roper can have up to six tendrils at a time. snip
Reel. The roper pulls each creature grappled by it up to 25 feet straight toward it. (SRD, p. 342, Roper)

A ruling that the assassin vine restrains anyone in the area who fails the DC 13 Strength save is also reasonable, given that the ability description isn't as specific as, for example, the T Rex and Roper descriptions.

It's not crystal clear

Another way to read the text is that of a serial encounter. Let's look at a party of four brave heroes: a cleric, a ranger, a barbarian, and a paladin. The first two are separated by 20' from the second two. The first two members step into the danger area and are subjected to the entangle / restrain problem. They both fail. The second two run into the area, and for whatever reason, the vine tries to entangle them ... hence the "use again" bit ... so the restrain / entangle ends on the first two.

Better to just kill the damned thing.