Brief summary

Courtesy of misterblue28: While sneaking, set the block where your feet are to glass. After releasing the sneak key, your hitbox and eye level will remain lowered, but otherwise you will behave as if not sneaking.

Some info

• This bug can be reproduced in snapshot 20w29a or release 1.16.1. I haven't tested this in any other versions (may change in the future as newer versions are released).
• It was difficult to search for this bug because the only summary I could think of was the really long one you see above, so I'm sorry if this duplicates any other reports.
• The screenshots taken that are directly embedded within the description were taken in release 1.16.1.
• Sorry if the images are resized strangely; I'm not too sure why that's happening.
• This relates to many reports, so I'll explain all relations here:
  • MC-157183 is slightly different than this report as that report deals specifically with doors; also, that report mentions that the speed of the player is reduced while in that position, unlike this report.
  • MC-181404 contradicts MC-157183 by stating that speed isn't affected by crouching in the door.
  • MC-131942 is different than this report because when the player released their crouch key, their appearance reverted to standing up. The appearance in this report is locked until the block is broken or the player moves out of the block.
  • MC-148390 is different than this report because this report is about the appearance of the player in third-person view more than their hitbox; yes, this report is about hitboxes but talks about the relationship between the hitbox and third-person view.
  • MC-165423 is included in this report, and the method described in that ticket is now obsolete. This contains more information (including new reproduction steps). I'll link the video included in that report here
  • MC-149259 relates to MC-165423, and the same relations apply.

The bug

If a solid transparent block* (that confused me, so it might confuse you; take a look at the links at the end of the report to learn more) is forced into the space where the player's feet are located, then the player's hitbox remains the same size as a sneaking player's, even though the player, seen from third person view, is shown as not sneaking anymore.

While in this state, the player can walk at normal speed, even while their hitbox is shortened. This can be used to their advantage in a PVP situation where a tiny difference in hitbox sizes can make a huge difference.

When the block described above is broken, the camera shifts upwards (as if the player was leaving sneak mode), even though the rendered player does not change at all (but the hitbox reverts to its normal size).

How to reproduce

1. Place a wooden pressure plate with 10 redstone ticks of delay in repeaters coming out of it:
   
2. Place a command block (Impulse, Needs Redstone) at the end of the repeater chain:
   
3. Insert the following command into the command block (note that glass can be replaced by any solid transparent blocks*):

   execute at @p run setblock ~ ~ ~ minecraft:glass
   

4. Stand on a block that isn't part of the contraption you've built.
5. Enter third-person view mode by pressing F5 and enable hitboxes by pressing F3 + B (note: keybinds may differ): 
   
6. Throw an item onto the pressure plate while sneaking (set to left shift by default) and wait for the redstone signal to reach the command block.
7. When the block is set, notice how player appears to have stood up, but the hitbox is still shortened (and notice how player can now walk at normal speed instead of sneaking speed).
8. Release sneaking key, and notice how nothing changes.
9. Break the solid transparent block, and notice how hitbox expands and camera shifts upwards, even though the player doesn't appear to have changed in any way.

Alternate reproduction method

Instead of using a command block to insert the block, the player can surround themselves with solid blocks and then, using a piston or a one-tick sticky piston, push the glass block into themself. The same results can be achieved, replacing steps 1-3 above; steps 4-9 must still be followed.

Footnotes

• Opacity (solid transparent block): https://minecraft.gamepedia.com/Opacity 
• *note: full-block solids, non-full-block solids, and solid mechanisms, as shown on this wiki page, are all considered solid transparent blocks for the simplicity of this report.