5e Monster design: When do monster hit dice matter?

[No brains]

What are the occasions when the number of HD a monster has will really matter? Sure it modulates hp in relation to a creature's size category and constitution (and sometimes its class levels), but what else should be considered when assigning a monster HD?

More HD allows for more short rests, even if most DMs don't need to worry about that. This can be useful for creatures that might retreat and rest when the party is resting, creatures allied to the party, and creatures that emulate short-rest recharging abilities.

More HD makes it harder to cast Imprisonment on a creature. Are there any other spells that relate to HD?

Can anyone tell me of any other practical applications to knowing how many HD a monster has or should have?

[Dualight]

It matters when PCs have means to turn into those creatures, and when effects that utilise Hit Dice, like wither and bloom come into play alongside those monsters.
This is especially important for Moon druids at higher levels, as they can stay Wild Shaped beyond an entire short rest, with higher hit dice, letting them heal more effectively and stretch the bonus health from Wild Shape even further.

[Cheesegear]

Can anyone tell me of any other practical applications to knowing how many HD a monster has or should have?

I use it as a range sometimes.

Sometimes my party will obliterate a monster in the few rounds, usually from lucky crits and high damage rolls. A monster with, for example 4d8 HD, will have 20 Hit Points...But there's no reason it couldn't have up to 32, if you wanted it to.

A Young Black Dragon has 127 Hit Points. According to the numbers, it could have up to 195 (15d10 + 45) Hit Points...If you want the fight to be more brutal, and/or the fight isn't as brutal as you want it to be. But, as always be real careful when you increase Hit Points because increasing Hit Points does have a four-fold effect. I'm not saying you need to bump the Dragon's Hit Points all the way up to ~200...But if you want an extra round in the fight, increasing the HP to ~150 doesn't hurt.

The other thing is, when you're a tough DM, if the party needs to retreat for any reason, they'll probably have a Short Rest after... The monster gets the same thing. If the players want a Round 2 (figuratively speaking), it's only fair, no?

I haven't used a creature's HD for anything other than those two things. Increasing Hit Points within a fixed range, and Short Rests.

[No brains]

It matters when PCs have means to turn into those creatures, and when effects that utilise Hit Dice, like wither and bloom come into play alongside those monsters.
This is especially important for Moon druids at higher levels, as they can stay Wild Shaped beyond an entire short rest, with higher hit dice, letting them heal more effectively and stretch the bonus health from Wild Shape even further.

What are the wither and bloom effects from? What do they do?

Wild shaping is an interesting point. HD number would be especially important to designing beasts (and to a lesser extent, elementals).

[Dualight]

Wither and bloom is a 2nd level necromancy spell introduced in Strixhaven: A Curriculum of Chaos that has multiple effects, the relevant on is that it allows you to target 1 creature in the AoE to spend hit dice(spell level - 1) to recover hit points equal to the number rolled + the caster's spellcasting ability modifier.

[Envyus]

I like to roll for monster HP. So that’s why it’s useful to me.