I would recommend to use NestJs as you have mentioned to make a simple application. As NestJs is easy to use and it uses Typescript. Additionally you can use mongoose with NestJs for MongoDB. Spring is awesome in case you need to develop a very complex and large application.
I also recommend NestJS based on your description. Same language as the front end which is good as there are only two of you, and the structure of NestJS apps is inspired by Angular so it will feel very familiar. JWT and MongoDB also well supported (obviously that's the same for Spring too though).
We use it for all web applications, it's a great framework.