Can you clarify what you mean by "it gives an error using web request blocking"? What is erroring and what does the error say?
On the extension platform side, there are two messages that come to mind that you may be referring to, both of which appear in the the chrome://extensions/?errors=<EXTENSION_ID> page for an extension.
First, if your extension includes the webRequestBlocking permission in it's manifest, you will see a message that says "'webRequestBlocking' requires manifest version of 2 or lower". This message is a warning, not an error; it doesn't prevent your extension from installing or running.
Second, if you attempt to register a blocking webRequest listener in the root scope of your extension's service worker, you may see an error message that says "Unchecked runtime.lastError: You do not have permission to use blocking webRequest listeners. Be sure to declare the webRequestBlocking permission in your manifest." This error will only appear when a Manifest V3 extension in Chrome is not force installed and attempts to register a blocking webRequest listener.
While this is a legitimate error – the event registration did fail – it should not prevent the extension's service worker from installing as expected. Unfortunately it's not currently possible to
This error is logged asynchronously, so it will not block the registration of your service worker. Unfortunately, since event listeners must be registered on the first turn of the event loop, there's no way to avoid this error (
crbug.com/1344312). That said, you can use chrome.permissions to asynchronously detect that the extension doesn't have the "webRequestBlocking" permission and use this signal to react as appropriate.