fix(browser): stop using deprecated dismissVC/presentVC #5599

Job	Run time
setup (ubuntu-latest)	53s
setup (macos-15)	1m 23s
lint-scripts	34s
lint (browser)	41s
verify-ios (/Applications/Xcode_26.0.app, browser)	1m 40s
verify-android (browser)	2m 8s
verify-web (browser)	40s
	7m 59s

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