Our DM has allowed us to play-test the summoning spells which appear in Unearthed Arcana 2020: Spells and Magic Tattoos. I'm playing a druid, and have added the 2nd-level spell Summon Bestial Spirit (pp. 3-4) to my spell list.
I chose the Circle of the Shepherd, whose 6th-level feature, Mighty Summoner, is meant to enhance a druid's summoning/conjuring spells by adding +2 HP per Hit Die and causing the damage to be classed as magical (XGE, p. 240).
For example, with the 3rd-level spell Conjure Animals (PHB, p. 225), if I conjured a Giant Boar (MM, p. 323), it would have an additional +10 HP because it has 5 Hit Dice (5d10 + 15), so the conjured/summoned creature would have 5d10 + 15 + 10 HP in total.
The relevant parts of the UA Summon Bestial Spirit spell description state:
You call forth the spirit of a beast. […]
At Higher Levels. When you cast this spell using a spell slot of 3rd level or higher, the creature assumes the higher level for that casting wherever it uses the spell’s level in its stat block.
The Bestial Spirit statblock that follows lists its HP as:
Hit Points equal the beast’s Constitution modifier + your spellcasting ability modifier + ten times the spell’s level
In the case of Summon Bestial Spirit, the creature's HP is linked to the spell level, so how does it interact with the Shepherd druid's Mighty Summoner feature? Does the spell level determine the Hit Dice?
I would appreciate an answer with an example and/or experience of having play-tested this spell.
By RAW they do not interact
As you note, the summoned creatures in the UA do not have hit die. Therefore you can't have hp increase "per hit die".
A suggestion for your DM
Keep it simple. Perhaps say that the summoned creature's hit die is equal to the level of the spell slot that was used to summon it.