MMS 2024 and 2023 should work with the Intel Arc a770, providing it is selected as the GPU for the Import, Processing and Export options in the program settings, Device options tab.
Export times will depend on the video format/resolution - eg 4K UHD 3840 x 2160 exporting as AV1 or HEVC require significantly more 'horsepower' than FullHd 1920 x 1080 AV1, HEVC or 4KUHD h.264/AVC, which in themselves require more 'horsepower' than FullHD h.264/AVC encoded.
However - certain effects applied to the video formats stated above are processed using the CPU and are not hardware accelerated on the GPU's, irespective of the Device options settings.
In it I mention that I emailed Magix support asking them about their tests with MS2024, Intel GPUs and Nvidia GPUs. In an attempt to encourage them to answer I did mention that I suspected they couldn't really comment and give suggestions.
Their reply was "As you say, we don't usually give advice on hardware. What I can say is that we have done the best performance tests with INTEL cards, followed by NVIDIA cards" so I was all set to buy the Intel ARC 770.
However, my son gave me his "old" Nvidia RTX 4060 and so I obviously saved a few pennies and didn't get the Intel.
Intel update their drivers at least once a month, I've found a noticeable improvement with my UHD770 GPU chip on my CPU - it's much more stable.
I only use my computer for video/music editing and similar activities; no gaming.