Thank you kindly for your thoughtful reply, and added info.
Re: "I would like to source an inexpensive Auracast transmitter dongle to connect to the audio source and a matched receiver to connect to my iPhone lightning connector to then be streamed to my aids".
Sorry, I do not know of any such dongle. You may want to try enquiring from a store that sells such equipment.
I understand the use of Auracast technology allows for streaming to multiple devices at the same time .... yet seems that requires equipping every participating device with the correct dongle!
AirPlay software on Apple devices can play audio across multiple speakers throughout a home in perfect sync.
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Apple publish a long list of bluetooth equipped hearing aids that are compatible with iPhone and iPad.
Those marked with an asterisk (*) beside are also compatible with Mac computers equipped with the M2 and M3 chip (and some of those with M1 chip). (ie: This enables watching movies, games, tv series etc. using the Apple TV app.)
List of Made for iPhone hearing devices
More info: Use Made for iPhone hearing devices - Apple Support
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Apple's AirPods, if suitable for your needs, may be comparable in cost to buying a dongle. While not hearing-aids, AirPods can perform some hearing-aid functions for those with limited hearing. As well as for hearing tv etc., AirPods may be useful in other ways (Eg: "Live Listen" to conversations in noisy environments, using iPhone.) It seems AirPods may connect directly to most Bluetooth equipped audio-producing devices, including many tv's.
More info: Get started with accessibility features on AirPods
Eg: Non-Apple article: How to Connect Airpods to a TV
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Apple Store's iPhone Adapters: (You can check compatibility in the sidebar) Charging Essentials - iPhone Accessories - Apple
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Re: "Classic Bluetooth has some lag issues which reduces the sound quality".
While very noticable at first, seems most people quickly adapt to the slight discrepency between the moment the sound or word is produced, and the moment that sound reaches the ears.
You may be able to use data from an audiogram to set headphone accommodations and improve the accuracy and sound quality. See how to: Use audiogram data in Health on iPhone - Apple Support
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Troubleshooting, if needed: See what to do: If the sound from your wireless headphones cuts out or is distorted
or
How to: Resolve Wi-Fi and Bluetooth issues caused by wireless interference - Apple Support