The HFS+ (aka MacOS Extended) file system really should not be an issue since macOS still supports it.
The newer Macs, especially the M-series Macs, tend to have some compatibility issues with some older devices. This seemed really prevalent back in 2020 when the M-series Macs were first launched, but I haven't seen as many reports these days....perhaps Apple fixed it with an OS update, or people just moved on from their older external devices.
There also have been a lot of reports on this forum with people having issues with external drives on their Mac Studio systems, especially on the rear ports. Unfortunately it is unclear if there is any specific cause for all of these reports. Many times using a better quality USB-C Thunderbolt3/4 or USB3/4 cable has been known to help, while some others report connecting the drive to a USB3 hub has worked. Or connecting the device to the front ports.
The first question is whether the physical drive even is recognized by macOS. Check to see if the physical drive is shown in Disk Utility. You may need to click "View" within Disk Utility and select "Show All Devices" before the physical drives appear on the left pane of Disk Utility. If the physical drive is not seen, then the file system is not the issue. Even if the physical drive is seen, there still could be a lot of hardware & even software issues that may be preventing macOS from seeing and/or mounting the drive.
One software issue is whether you are using the LaCie software to manage the external drive on the old system, but have not installed that software on the new Mac (assuming the software is still compatible with Sequoia & an M-series Mac). FYI, it is best to just let macOS manage the external drives.
Is this external drive just a standard data only drive, or is it a backup drive? If the latter, is it a Time Machine backup drive?
Theoretically it should be possible to convert the HFS+ file system to APFS. You would need to use Disk Utility. On the Disk Utility "Edit" menu there is a "Convert to APFS...." option when you select the correct item on the left pane of the Disk Utility. This should not disrupt the existing data on the drive, but this is a major change so it is possible for data loss especially if something goes wrong midway through the conversion. You need to make sure you have a good backup of the data on this drive before you do anything.....hopefully you already have frequent & regular backups of the external drive & both of your computers.
Also, if this external drive is actually a Hard Drive as opposed to an SSD, then using the HFS+ (aka MacOS Extended (Journaled) ) file system is best since the APFS file system can cause performance issues with a Hard Drive and make the Hard Drive work even harder. If the external drive is an SSD, then either file system is fine although APFS is better optimized for an SSD and provides some new file system features as well.