If I use the Standard membership but then exceed my monthly submissions, can I switch to the paid-for access without losing any data?

First of all, the form you have shared is hosted in a guest account: https://form.jotformeu.com/62664102541347 

I have moved it to your registered account "katiebrunt". On regards of upgrading, do not worry, the data is not lost when you upgrade to a paid plan.

Let us know if you need more help.