From the source code:
Firefox: `${this.homedir()}/Library/Application\ Support/Mozilla/`,
Chrome: `${this.homedir()}/Library/Application\ Support/Google/Chrome/`,
"Chrome Beta": `${this.homedir()}/Library/Application\ Support/Google/Chrome\ Beta/`,
"Chrome Dev": `${this.homedir()}/Library/Application\ Support/Google/Chrome\ Dev/`,
"Chrome Canary": `${this.homedir()}/Library/Application\ Support/Google/Chrome\ Canary/`,
Chromium: `${this.homedir()}/Library/Application\ Support/Chromium/`,
"Microsoft Edge": `${this.homedir()}/Library/Application\ Support/Microsoft\ Edge/`,
"Microsoft Edge Beta": `${this.homedir()}/Library/Application\ Support/Microsoft\ Edge\ Beta/`,
"Microsoft Edge Dev": `${this.homedir()}/Library/Application\ Support/Microsoft\ Edge\ Dev/`,
"Microsoft Edge Canary": `${this.homedir()}/Library/Application\ Support/Microsoft\ Edge\ Canary/`,
Vivaldi: `${this.homedir()}/Library/Application\ Support/Vivaldi/`,
In this folder there is a subfolder “NativeMessagingHosts”, and in that subfolder a file “com.8bit.bitwarden.json”. This is the manifest.
By the pattern I would guess for thorium it would have to be copied to:
~/Library/Application Support/Thorium/NativeMessagingHosts/