We are having the same problem with video on Moodle 3.7.1 where videos will not play in the Moodle Mobil app or in Safari on an iPads. The same videos will play fine on a Moodle 3.6.3 site. The video format is not the issue. These two sites have identical media settings. However, they are hosted by two different services. I feel it is either server settings or version differences that are the cause of the problem. We have entered a support case with the hosting service to help determine the cause. I will report their findings when we get some more information.
Did you ever find a solution? I'm having this issue as well.
Fixed it! So I ended up uploading a different video size. The iPad does have limitations within some formats. For example, H.264 videos are limited to 1080 pixels and 30 frames per second. MPEG-4 videos are limited to 2.5 Mbps and 640 by 380 pixel resolution at 30 frames per second. Videos exceeding these limits may not play correctly on an iPad, or may not play at all. I had a H.264 video at 720 and it wouldn't play. So I used media encoder and actually made it bigger to 1080 and it worked!