A family of Microsoft relational database management systems designed for ease of use.
Access is NOT the tool for for an online database. I'm not sure what you think "switching to Office 365" will do for you. It really doesn't.
While there are ways to create an Access application that can work with the cloud, I'm not sure they can perform well. There are other ways to allow for remote data entry however.
An Access accdb file is limited to 2Gb in size. That's an absolute limit. However, one of Access' better features is its ability to connect to data sources that aren't Access tables in an accdb file. Using SQL Server or Azure (for example) as the back end can allow for much larger amounts of data. The 1TB of cloud storage that comes with Office refers to One Drive. One Drive, however, cannot be used to share Access data in a multi-user situation.
By design, Access is a multi-user application. But it is designed for use over a LAN and doesn't work well over a WAN or with the Cloud. If you have users that are all on a LAN, the data can be stored on a Server in either an accdb file or a different data source. Users then have a front end on their local PCs.
Other cionfigurations for remote access is using a Terminal Server or having users remote into a PC on the LAN.