https://backpack.tf/item/13881241363

https://backpack.tf/profiles/76561198119038933#!/compare/1747180800/1747267200

https://backpack.tf/profiles/76561199084784906#!/compare/1747180800/1747267200

Dumped in bulk alongside Scorching Flames Reel Fly Hat and Blooming Beacon Taunt: Roasty Toasty

https://backpack.tf/item/13967845378 - Hidden history

https://backpack.tf/profiles/76561198198896481#!/compare/1752105600/1752451200

https://next.backpack.tf/classifieds/snapshots/Prettiest%20Star%20Soft%20Hard%20Hat/6870ec2d2a0f5dee5d1ea8d9 62.14/1.09 = 57 key buyout

Seems to be 55 keys (other 86 keys + Showstopper Taunt: Commending Clap match to buyer of Strange Ignited Crest Berlin Brain Bowl)

Sales

55

https://steamcommunity.com/market/listings/440/Unusual%20Soft%20Hard%20Hat?filter=Prettiest+Star

https://marketplace.tf/items/tf2/31331;5;u320 - Barely outdated sale at $149.99/1.94 = 77 keys, seems high either way given lower unsold

https://stntrading.eu/item/tf2/Unusual%20Prettiest%20Star%20Soft%20Hard%20Hat

https://imgur.com/a/7ZR3AM6

https://backpack.tf/item/13881241363 - 62 keys

Taking 55 flat.