@Anonymous
First you can try and see if you would prefer a Power BI dataflow as I think it may be better suited for this kind of scenario. The Power BI dataflow should support Azure Synapse Analytics, SQL and SharePoint as data sources. With Power BI dataflow, you an integrate directly Azure Synapse Analytics and SharePoint without even a need of the SQL server as an intermediary. You may need a Power BI Pro license though, but it could be worth it if it saves time and gets you better results.
If you really prefer to use Power Automate, you should check what happens if you try and just place random hard coded values in there without SharePoint List Try using just a trigger called "Manually trigger a flow" and then in Update row. (V2) If this still fails, then the issue is only with the SQL part.
Try instead to Insert row and see if that works.
If that fails too (or even if the above works, actually, for that matter),
try to just Get rows (V2) and see if it is possible.
If Get rows (V2) works, try to look at the result and try carefully to Get row (V2) - if that works, then try Update row (V2) again.
Now let's suppose Get rows (v2) does not work. try Get Tables (V2) and based on that, try Get Rows (V2) again
If nothing else works and you prefer to use custom SQL to test it, try Execute a SQL query (V2) to test it.
If all of it fails, go to https://us.flow.microsoft.com/ -> Data -> Connections - delete the Connection - then go to https://us.flow.microsoft.com/ -> My Flows and make a new simple Flow like that. It should prompt you to sign in to make a Connection - do as instructed.
If even the above fails, check carefully the SQL Server related setup, the problem could end up being there even if you have read/write access.