Druid Spells: Conjure [X]
There are 3 Druid spells which work: conjure animals (3rd level), conjure woodland beings (4th level), conjure fey (6th level). Each of these conjure beasts, fey, or fey that take the form of beasts; either way, they count.
There are also two summon spells from Tasha’s Cauldron of Everything, specifically the beast and fey ones. Do note that both of these have a (non consumed) material component with a cost (200 and 300 gp respectively).
Non-druid spells: Find [X]
There are 3 non-Druid spells which can (unambigiously) work with these two features: find familiar (1st level), find steed (2nd level), and find greater steed (4th level). The former is probably the most relevant since it can be chosen with the Magic Initiate feat (choosing Wizard) while the other two require 5 or 13 Paladin levels respectively (multiclassing to Lore Bard may be preferable). Each of these summon a creature which is a celestial, fey, or fiend where choosing fey will let it work for us. (If applicable to your game, the flock of familiars spell from Lost Laboratory of Kwalish module will work as it is an extension of find familiar.)
These spells either require some favorable DM ruling and/or aren't very relevant to such a Druid.
Gate lets you summon some named creature. However this 9th level spell is not on the Druid spell list, meaning no amount of multiclassing will get you this spell and the features in question and you don't get any control over the summoned creature so giving it more hit points might not be in your best interest. The gate spell can be cast using a candle of invocation or cubic gate (DMG p. 157 and 160), however as these are very rare and legendary respectively it isn't exactly a reliable method.
This 9th level spell is on the Druid spell list, however the required target needs to not only be dead, have been dead for less than 200 years, not have died of old age, but also no longer have a body. The spell then creates a new body for it and so a creature can be argued to have been created by the spell and so qualify for the features. How many Beasts or Fey do you know fitting that description? And I hope it was worth the 25 000 gp and the frustrated look from your DM.
The two Wizard spells clone (8th level) and simulacrum (7th level) lets you make a copy of a creature. Clone lets you copy any kind of creature which animates when the original dies, while simulacrum lets you copy a beast or humanoid (only the beast part is relevant to us). Being high level spells not on the Druid list and the price tag in the material components make them of limited value to such a Druid.
My goal with this answer is in part to see if I missed any spells and I've found putting something wrong/incomplete on the internet is a good way to find the correct/remaining things.