Thank you, I think I understand now. Let me explain from a Bluetooth protocol perspective for AAC and hopefully make some sense of this:
Bluetooth uses the A2DP specification for delivering music on top of the various Bluetooth radio protocols (aka 4.x and 5.x). A2DP is an old standard that is being replaced with a (large) set of protocols/specifications branded as "LE-Audio." In the standard you have for "AAC":
1. Negotiation between e.g phone and TWS to see what is acceptable
2. Encoding/decoding
3. Wrapping the encoded sound in a format able to be sent over the radio protocol (technically: the media payload format)
In this case, I believe that the sound was being decoded using the 1997/1st specification of AAC (sometimes called MPEG-2 AAC, which isn't quite the later defined AAC-LC profile BTW). This is common in virtually all of the TWS since that is now out of protection so is free.
What is being referred to is the wrapping of the encoded sound (4.5.4 in the A2DP 1.3.2 spec) and what is needed to change the format of the stream to fit into the wrapping format. This is normal stuff, though granted the specification is a bit vague, so someone coming new to this may make some errors. It also isn't a "file" problem but between the bluetooth driver in the e.g. phone and the bluetooth decoder in the TWS. The only issue could be that the decoder in the TWS can't retransform the stream into a format the "AAC" decoder can use, but that would result in horridness easily picked up.
What isn't normal is fixed bit rate AAC. The TWS as the Bluetooth decoder must support variable bit rate "AAC" or it is not compliant with the spec. In other words, if the encoder decides to do variable bit rate in (1) then TWS must accept and decode it.
"AAC" being the same bitrate as AptX is possible from the spec viewpoint but again, it the encoder that determines the rate (all the TWS can do is reject it). In my experience this sounds a bit high as
https://www.aptx.com/aptx says 384Kbps and on TWS the "AAC" encoding is normally VBR around 200 Kbps. If you have a decoder (TWS) that can only do constant bit rate and not variable bit rate then you will get glitches though for some content I'm pretty sure you won't notice it.
Also, you'll note I put AAC in quotes. This is because AAC is a spec that has constantly evolved since the first one in 1997 and AAC refers to the whole specification which is a toolbox of many, many, many tools. You implement a profile of AAC (as with other MPEG based specifications like the video ones) and that's what you refer to, so just saying "AAC" for an implementation is meaningless from an engineer or sound quality/bit perspective. Sadly, the Bluetooth A2DP spec, which is coming up for 20 years old, was done at a time when AAC was way less complicated so was also imprecise with wording to further compound this issue.