Stuck in starting page

Ok - this method will mean all personal data will be lost and can not be recovered.

1 - Restart the computer as per directions in the following link How to erase an Intel-based Mac

2 - How to reinstall macOS and read all the directions

3 - This will probably install Yosemite or whatever version of macOS associated with the Recovery Volume

4 - once the OS is installed Yosemite ??

5 - Use this link to Download and install High Sierra. Suggesting High Sierra as it will download and Install any Boot ROM required and also convert the internal drive to the newer APFS / GUID format required to install Big Sur.

6 - Once High Sierra is installed and all addition Security Updates have also been installed.

7 - Decide if Big Sur is suitable for this computer. Generally - at least 8 GB RAM and 256 GB SSD drive will work.

8 - Still sure Big Sur is the End Game Tips How to Upgrade to Big Sur - Read through the tips to make the upgrade as smooth as possible

What version of macOS was existing Before the download of Big Sur ??

How much Empty Space was available Before the attempt to upGrade to Big Sur??

What are the System Requirements ie: Empty Space Requirements specific to the Big Sur. Apple States Requiring 35.6 GB of Empty Space but suggest 50 GB

Are there any AntiVirus, Disk Cleaner, Optimizers, Un-installers, etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal operation of the OS and may even Corrupt the OS requiring a Reinstallation. 

Have you attempting booting into Safe Mode This may or may not allow the upGrade process to complete - hopefully successfully.

You did do a Time Machine Backup Before attempting the upgrade to Big Sur - please, really hope so.

Would like to suggest possible solutions but need to know before moving forwards as next steps might involving loose everything on the drive.

Am on my iPhone right now. Question, do you use two factory authorization?

Is there an Active and Functional Internet Connection during the process in you picture above. Without it, the message appear would back total sense - the computer can not reach the Apple Servers

Welcome and Thank you too !

Lessen learned - alway keep at least 15% of the Total Capacity of the drive as Empty Space.

Example: Drive Capacity is 128 GB x 15% = 19.2 GB as Empty Space.