qfield.cloud is exactly what you're looking for. It is natively supported in QField and allows you to synchronise your field survey directly to the cloud (and to your team) as soon as you have connectivity. This way you can work with no issues wherever you need to.
Once synchronised, you can use your data with QGIS, or any other tools you wish. Later we'll also add the possibility to directly publish your data on a web map from the QFieldCloud web panel.
We are currently in beta and are opening up spots every day to new preregistered users. If you preregister on qfield.cloud you'll get an information mail very soon, and if you reach out directly to us at opengis.ch you might even get an immediate invitation ;)
you can also checkout my [1h] talk about it on QGIS's youtube channel
Disclaimer: I'm one of the developers of QField/QFieldCloud