Sometimes, local development environments can have caching issues or other peculiarities. Try deploying your project to a staging or live environment to see if the GTM tags work there.
Open your project in a browser and use developer tools (usually accessible via F12 or right-click -> "Inspect"). Check the "Network" tab to see if the GTM script is being loaded.
Look for any errors in the "Console" tab that might indicate issues with the GTM setup.