Dell Express Flash P4510 - Firmware Update

Dear Team, recently I bought multiple Dell Express Flash P4510 4TB U.2 SSD drives. Still originally packaged, manufacturing date 2019. Currently built into a Lenovo ThinkStation P510, SSDs are visible by operating system and could be used.

However, I would like to update the highly recommended firmware first: https://www.dell.com/support/home/de-de/drivers/driversdetails?driverid=gd4x4

Firmware on SSDs: VDV1DP21

Recommended Firmware: VDV1DP25

The firmware update software of Intel/Solidigm doesn't work, the following message is shown: No known update for SSD. If an update is expected, please contact your SSD Vendor representative about firmware update for this drive.

What can I do to update the firmware successfully?

Is there an option to install the Intel/Solidigm-Firmware?

Regards

P.S.: wrote this in the (inactive?) German forum first: https://www.dell.com/community/en/conversations/storage/dell-express-flash-p4510-firmware-update/66ac0fbc47effa74c4831f73