roughly speaking, you ignored the node_modules folder on branch a, and you must have executed the npm install command on branch a, but not on branch b. Gitignore did not ignore the folder node_modules, or should you not execute the npm install command?
is a bit of a mess. I guess you are doing micro services, right? the whole large project has multiple sub-projects, and each sub-project has its own directory, and each directory has its own independent node_modules folder, so that you switch branches and directly enter the directory operation of this sub-project.
the file directory is roughly as follows:

project_all
    -- project_a
        -- node_modules
        -- src
        -- package.json
    -- project_b
        -- node_modules
        -- src
        -- package.json
    -- project_c
        -- node_modules
        -- src
        -- package.json
    .gitignore

I hope I can help you.

then you commit when switching branches.

first of all, the basic branch should be called "master".