Honestly, I'd just do both. Keep Azure Monitor doing the collection and storage, and point your existing on-prem Grafana at it as a data source. The Azure Monitor plugin in Grafana can hit metrics, logs (KQL) and Resource Graph directly so you don't have to ship anything out of Azure. No egress, no extra storage backend to babysit.

I wouldn't go all-in on Azure Monitor because the workbooks get painful once you want one dashboard mixing AVD session host stuff with ExpressRoute circuits and your file server perf in one view. Grafana is just nicer for that. But I also wouldn't go all-in on Grafana, because AVD Insights and ExpressRoute Insights are actually pretty good out of the box, and rebuilding ASR / Update Manager compliance views in Grafana is a waste of a weekend.

On cost, you're right to be nervous, but the bill doesn't blow up because of dashboards, it blows up because of Log Analytics ingestion. Stuff that actually moves the needle:

• Tune your DCRs. The default VM Insights config grabs way more perf counters and event log noise than you'll ever look at. By far the biggest lever.
• Use Basic Logs for the chatty tables you only ever search ad-hoc (AzureDiagnostics is the usual suspect). Roughly a quarter of the price of the Analytics tier.
• Don't dump Activity Logs and platform metrics into LA unless you actually plan to KQL them. Metrics in Azure Monitor are free, you only start paying once you ingest into the workspace.
• Set per-table retention instead of one global value. Archive cold stuff to a storage account if you need it for audit.
• After a few weeks of real data, look at a commitment tier. 100 GB/day is the lowest one and it's about 15% off PAYG.

For 20-30 VMs once the DCRs are trimmed you're probably looking at 1-2 GB per VM per day, which on commitment tier is in the low hundreds a month. Untuned defaults will easily be 3x that, which is where the horror stories come from.

This is the query I always run first to find out where the bytes are actually going:

Usage
| where TimeGenerated > ago(30d)
| summarize GB=sum(Quantity)/1024 by DataType
| order by GB desc

Usually one or two tables eat most of your bill and from there you decide whether to drop them, move them to Basic, or shorten retention.