An Azure analytics service that brings together data integration, enterprise data warehousing, and big data analytics. Previously known as Azure SQL Data Warehouse.
The Synapse Studio UI does not let you change the Spark version of an existing pool. This is by design and is officially confirmed in the Microsoft Learn
https://learn.microsoft.com/en-us/azure/synapse-analytics/spark/apache-spark-version-support
As you can see it is indicated like : "This isn't allowed from UX, customer can use Azure PowerShell to update Spark version. Use 'ForceApplySetting', so that any existing clusters (with old version) are decommissioned."
Your assumption that "you can't delete a pool if it's connected to a notebook" is actually not correct. In Synapse, notebooks reference a pool by name. You can delete the pool; the notebooks remain intact and will simply fail to run sessions until a pool with that name exists again.
for solution of you do not have powershell or git you can go with REST API option
for REST API no powershell module install required.
this link may help:
or alternative you can use cloud shell if your policy is to block powershell locally you can use this sessions from brower s well
https://learn.microsoft.com/en-us/powershell/module/az.synapse/update-azsynapsesparkpool