With inspiration from the Obsidian snippet described in Clip selection to Obsidian - #2 by nick I have written an Obsidian snippet which executes a search of a specific Obsidian vault - just change the vault name as appropriate:
# PopClip - Obsidian Serach
name: OBS-Search
icon: O-S
options:
- identifier: vault
label: 'Vault Name'
type: string
capture html: false # this is needed when we want markdown text
javascript: |
const vaultName = encodeURIComponent(popclip.options.vault)
const search1 = encodeURIComponent(popclip.input.text)
popclip.openUrl(`obsidian://search?vault=${vaultName}&query=${search1}`)
#end