You can play FLAC. That does not make Bluetooth lossless.
MP95 can decode a local FLAC file and send the resulting audio to the iPhone's selected output, including connected AirPods. Ordinary Bluetooth listening from an iPhone does not preserve the FLAC stream unchanged. The phone handles the wireless connection; choosing a different player does not turn that connection into a USB cable.
Apple's lossless-audio documentation distinguishes ordinary Bluetooth from supported wired AirPods Max connections and certain AirPods connections to Apple Vision Pro. A Vision Pro exception is not a promise of wireless lossless playback from your iPhone. Check the exact headphone model and connection, rather than relying on the word AirPods alone.
Is there a reason to keep the FLAC files?
Yes: they remain useful originals for your collection and for listening through other outputs. Playing a file over Bluetooth does not rewrite the stored FLAC as AAC. The same file can later feed a wired setup without another download.
The trade-off is storage. If your only listening route is wireless earbuds, filling a small phone with large hi-res files may not buy you the benefit you expect. Keep a backup of your originals before making smaller listening copies. Converting a lossy source into FLAC will not restore information already discarded.
What is worth adjusting in MP95?
Start at a comfortable volume with EQ and effects off. Then change one thing at a time. A small EQ correction can be useful even when the final connection is lossy. Saturation, crossfeed and 8D deliberately alter the sound; use them because you like the result, not as steps toward lossless playback.
MP95's sample-rate matching is relevant to supported output routes such as a USB DAC. It cannot force AirPods to accept the source file's rate over a different wireless protocol. Likewise, the file's 96 kHz label is not evidence that the earbuds receive 96 kHz audio.
If you want a wired lossless route
Check Apple's current compatibility notes for your AirPods Max model and cable, or use compatible wired headphones with an appropriate DAC. For an external DAC in MP95, compare the file's sample rate with the actual output information and disable processing if your goal is unchanged samples.
Lossless delivery and audible preference are different questions. Headphone fit, background noise and mastering can matter more to a listening session than the badge beside a filename. You can keep the lossless original without treating every wireless session as a failed hi-fi test.