Merge pull request #10076 from dolthub/tim/checkout-in-agent-md

Add a dolt checkout section to AGENT.md

Author: timsehn

go/libraries/doltcore/doltdb/AGENT.md

@@ -45,6 +45,13 @@ dolt checkout <branch-name>
 dolt checkout -b <branch-name>
 ```
 
+### Checkout Behavior with Running SQL Servers
+- `dolt checkout` on the CLI only affects the shell process that runs the command. When a `dolt sql-server` is running, existing SQL connections keep their current branch until they explicitly switch.
+- Each SQL session (CLI `dolt sql`, MySQL client, application connection) maintains its own active branch. Run `CALL dolt_checkout('<branch>');` at the beginning of every session or scripted block to ensure you are on the correct branch.
+- Chain branch changes inside scripts: start with `CALL dolt_checkout('<branch>');`, then run your queries. Do not assume a previous checkout persists for new connections.
+- When automating, include the checkout in the same transaction / session context where the data changes execute.
+- A good way to make sure a `dolt sql` session connects to the br1 branch for instance is `dolt --branch br1 sql`.
+
 ### Data Operations
 ```bash
 # Stage changes