The bug
The block and item model files for air do not define any textures at all, not even for particles.
While this does not cause any errors to be logged (although it should - see MC-236295), it does result in missing textures manifesting when using certain commands pointing to air (MC-239407). The issue isn't with the command itself as is stated by a former Mojang employee in the comments, but with the fact that there is no model defined for air.
The missing texture should never be visible unless resource packs are misconfigured, and this is a rare case where this is true in vanilla.
How to fix
A resource pack is attached to this ticket that fixes the issue entirely. To fix the issue in vanilla, simply add in the air texture file, as well as the modified model files.
Related issues
relates to
Attachments
Comments

Can confirm, checking the block model for air (air.json):
[media]

Use the command /particle minecraft:block_marker{block_state: "minecraft:air"} for 1.20.5-pre1 and onwards.

24w45a now explicitly specifies minecraft:missingno for the air particle. Should this be resolved as Fixed and a new ticket created?

I've reported the new behaviour under MC-278165.