chore: fix docker test workflows (#4308)

# Description

## Problem\*

Resolves <!-- Link to GitHub Issue -->

## Summary\*

This adds a change which didn't make it into #4306 so that we only run
node tests on the node image and vice versa.

## Additional Context



## Documentation\*

Check one:
- [x] No documentation needed.
- [ ] Documentation included in this PR.
- [ ] **[Exceptional Case]** Documentation to be submitted in a separate
PR.

# PR Checklist\*

- [x] I have tested the changes locally.
- [x] I have formatted the changes with [Prettier](https://prettier.io/)
and/or `cargo fmt` on default settings.

.github/scripts/integration-test-browser.sh

@@ -2,4 +2,4 @@
 set -eu
 
 ./.github/scripts/playwright-install.sh
-yarn workspace integration-tests test
+yarn workspace integration-tests test:browser

.github/scripts/integration-test-node.sh

@@ -2,4 +2,4 @@
 set -eu
 
 apt-get install libc++-dev -y
-yarn workspace integration-tests test
+yarn workspace integration-tests test:node