Backups of MacBook Pro - .Spotlight-V100

I have a MacBook Pro that is less than a year old, with Apple M2 Pro chip, running Sonoma 14.2.1. Prior to this I had an MBAir which I traded in AFTER doing MBAIR to MBPRO migration.

I have attempted to use the same external hard drive to back up the new computer, to no avail. I keep getting the message that there is not enough space on that external hard drive to do this but, in Finder, info on the folder reveals that there is a 370+ GB capacity.

I do not have the option to delete nor can I access the Spotlight-V100 folder because, apparently, I do not have 'permission' to do so.

Please just let me know how I can clear this space to start doing backups.

Many thanks.