Is there a way to only receive errors for our own code, and not for 3rd party libraries?

Yes, you can set up a thirdPartyErrorFilterIntegration as instructed here. It allows you to filter out errors originating from third parties, such as browser extensions, code-injecting browsers, or widgets from third-party services that also use Sentry.

Please note that this option is available in browser-based SDKs from version 8.10.0 and above, and only if you are using a bundler and one of Sentry's bundler plugins.