[BACKEND] Add functionality to booking creation popup and integrate into page

[bcho892]

Is your feature request related to a problem? Please describe.

Following the work done in #473 we should make it call the actual endpoint (in #380) and integrate it on the front end.

BEFORE MERGING

• [ ] Integration test written for services
• [ ] Schemas annotated if adding new models
• [ ] Code generation run (hint: yarn workspace server tsoa spec-and-routes)
• [ ] Appropriate mocks created where possible
• [ ] PR Reviewed (For non-trivial changes)
• [ ] Changes tested after rebasing on master or merging in master (hint: git fetch origin master:master, then git rebase master or git merge master)
• [ ] All required PR checks passing