@MatthewWalters1, adults wear the Eagle Scout medal only at formal Eagle occasions. In my opinion, Scout Sunday does not fit that.
I do think Scout Sunday is a formal occasion. Obviously, anyone holding the National Duty to God Award should wear it, particularly since there is no square knot cloth emblem for it. I haven’t known of any restrictions on adults wearing religious emblems earned as a youth since the late 1980s. At that time, the thinking was rebooted. Youth and adults became eligible for the youth religious square knot for emblems earned as a Cub Scout. Prior to that time, Boy Scouts could not wear Cub Scout religious emblems on their uniforms. The medal was removed from the bar on which it hung, and only the bar was worn. When this all got erased, I believe there was clarity that adults could wear the emblems they earned in their youth.
In recent years, the Guide to Awards and Insignia has indicated that religious emblems earned through membership in another organization such as Girl Scouts of the USA or Campfire USA could also be worn on BSA uniforms. So, some adults (and maybe even some youth) may have these and should be encouraged to wear them.
I would encourage anyone (youth or adult) with the Venturing Trust Award to wear it on Scout Sunday. Other Venturing awards such as Ranger and Quest may also be worn by adults. When they last appeared in the Guide, the Venturing Gold and Varsity Denali Awards were to be worn only by youth. Similarly, the National Medal for Outdoor Achievement is only for youth.
The highest awards/ranks in older youth programs: Quartermaster, Venturing Summit, Venturing Silver, Explorer G.O.L.D., Air Scout Ace, Explorer Silver and Explorer Ranger are appropriate for wear at any formal occasion. The Young American Award (if earned before August 1998) is in this category as well, but it is a pendant worn on a ribbon hanging around the neck, so your modesty must allow for it to be worn. The Explorer Achievement Award is the final award in this category, and it is a small round lapel pin that goes directly through the shirt and should be fine to wear above the left pocket seam on any occasion. Starting in August 1998, the Young American Award was decoupled from the traditional Scouting program, and should no longer be regarded as an award appropriate for wear on a BSA uniform.
Of course, training awards and special awards earned by adults and worn around the neck are appropriate for formal occasions like Scout Sunday. For awards earned by youth and worn around the neck, if something can also be earned as an adult, like the Venturing Leadership Award or the Order of the Arrow Distinguished Service Award, this should be fine for an adult to wear, even if it was earned as a youth. Supernova around the neck awards are not worn by adults, The only Supernova award worn by adults is the gold bar representing the Einstein Gold Award.
As has been stated above, whether Scout Sunday is a formal occasion is a judgement call. However, it appears to me to be so more often than not.