I linked a bunch of Bash stuff here. Sorry if that's off the mark but the points made are almost all *nix and shell flavor agnostic.
So you are looking to read an environment variable form a shell running in one of Vim's terminal buffers. Unfortunately, such variables are located in the shell process's memory and the internals of a process, including said memory, are locked down tight from access by other processes...for obvious security reasons. This holds
true even for the process that created it (the "parent"). Yes, a child inherits a lot
of things from the parent when it is created but that's a one way mechanism and there's no other inherent capability allowing the parent to see what's going on inside it while it's running1. Going the other way a child process can never affect any part of the parent's environment, which includes its variables, its current working directory, its open files, its resource limits, etc (BashFAQ 060)
The story doesn't end there, though. Obviously processes can communicate with each
other. Typical mechanims for this are shared memory, sockets, and named pipes aka FIFOs.
Vim doesn't provide anything that's directly relevant but if you're determined then you can fairly easily set something up yourself in Vim and the child shell. The simplest approach would have to be to just have the child dump the data of interest into a temporary file and have Vim read it from there. If you're not dealing with production systems or anything serious like that you might want to go that route.
Or if you want to try something a little more complex you could look at FIFOs which are pretty accessible in shell scripts (thus the above link to some relevant info). Also, one of the things a child inherits is the parent's open file descriptors so that might be useful...in combination with FIFOs or otherwise.
1The parent does have some lifecycle control, can send signals to the child (hello
kill) and can read its exit code upon termination...none of which help here. (Note that I'm ignoring various hacks and other risky behaviors as well as debuggers and the like to avoid a trip into the weeds.)
For a bit more discussion around Vim, shells, parent-child relationships and inheritance see Why does !cd not change the directory. For a deep dive beyond Vim, check out Bash Process Management...chock full of juicy details.