Keep the fields filled in after submitting the form

It is not possible by design to repopulate the fields. From my observation, CF7 issues a javascript reset function on the form.
You can

1- Modify the cf7 plugin for your needs like this https://www.ads-software.com/support/topic/how-to-not-clear-or-autofill-certain-fields-after-submission/

2- Have a look at this workaround here https://stackoverflow.com/a/67122233