iMovie will not log in into YouTube

Welcome to the Apple Support Communities!
I understand you recently made some changes to your YouTube channel, and updated your iMovie software, but you are no longer able to export your iMove projects to YouTube. Are you getting an error message from the iMovie application or from the YouTube website? What is the exact error message?
One way to address this issue is to export your movie project to a folder on your Mac or to an external drive. Then, access the YouTube website via Safari, sign in to your YouTube account, and then upload the file directly. If you are not able to sign in to your account this way, then you know the issue is with YouTube and not the iMovie application. This workflow also provides you with a copy of your movie for backup purposes.
Looking at the YouTube support website, I noticed there has been a change to the sign in process. You no longer sign in with your YouTube username, but with your YouTube or Google Account email. I wonder if this may be part of the issue?
Can't sign in with YouTube username - Google Support

If you're having trouble signing in with your YouTube username, try signing in to your account by entering your full email address. Then, enter the same password you’ve been using to sign in to YouTube.

You're still signing into the same account as always—you just need to enter the email address on the account instead of your YouTube username.

Why do I need to sign in to a Google Account on YouTube?

You access YouTube with your Google Account. The password you've used to sign in is your Google Account password.

As we integrate services across Google, we no longer support signing in to Google Accounts with YouTube usernames. Instead, you need to sign into YouTube with your Google Account email address (this is often Gmail, but can also be a different domain like Yahoo, Hotmail, etc.). Learn more about using your Google Account for YouTube.

But I don’t like my Google Account email address!

• If you're using a Gmail address, you can add an alternate email address to sign in with.
• If the email address you use isn't a Gmail address, you can change your email address. Or, you can replace it by adding Gmail to your account.

Some old YouTube channels (created before May 2009) are not part of a Google Account. Find out how to access a YouTube channel that's not part of a Google Account.

You mentioned you are working with iMovie for Mac. If you use any third party software with YouTube, you will need to create an app-specific password for it:
Using app-specific passwords
Enjoy your day!