Never mind, we managed to fix it this morning.
The fix entailed copying mssql-jdbc-7.4.1.jre11.jar to Mendix Studio Pro 8.7.0 install directory’s \runtime\bundles directory (In our case it is “C:\Program Files\Mendix\22.214.171.1246\runtime\bundles\”)
This in essence “overrides” the reference to com.microsoft.sqlserver.mssql-jdbc.8.2.0.jre11.jar, which ships with the 8.7 upgrade (Mendix 8.6 shipped with com.microsoft.sqlserver.mssql-jdbc.7.2.1.jre8.jar).
Regarding Andrej’s comment on the answer (and for completeness sake) :
When deploying to a server environment, the same “fix” applies, but the directory where the mssql-jdbc file needs to go is in the Mendix Server distribution install location under ...\Servers\server version\runtime\bundles\