ライブラリの写真をPHAssetで取得して、UIImageで更新保存するサンプルです。
ググっても意外と出てこない模様なので。

ちゃんと読もう

Apple 公式のサンプル

環境

Xcode 13.0

ミニマムなサンプルコード

import UIKit
import Photos

private lazy var formatIdentifier = Bundle.main.bundleIdentifier!
private let formatVersion = "1.0"

private func update(asset: PHAsset, toPhoto: UIImage, completionHandler: @escaping ((Bool, Error?) -> Void)) {
    let options = PHContentEditingInputRequestOptions()
    options.canHandleAdjustmentData = { _ in
        return true
    }
    asset.requestContentEditingInput(with: options) { input, info in
        guard let input = input else { fatalError("Can't get the content-editing input: \(info)") }
        
        DispatchQueue.global(qos: .userInitiated).async {
            let output = PHContentEditingOutput(contentEditingInput: input)
            let adjustmentData = PHAdjustmentData(formatIdentifier:formatIdentifier, formatVersion:formatVersion, data: "my app".data(using: .utf8)!)
            output.adjustmentData = adjustmentData
            
            let jpg = toPhoto.jpegData(compressionQuality: 0.9)
            
            do {
                try jpg?.write(to: output.renderedContentURL)
            } catch let error {
                fatalError("Can't save image to PHContentEditingOutput.renderedContentURL : \(error).")
            }
            
            PHPhotoLibrary.shared().performChanges {
                let request = PHAssetChangeRequest(for: asset)
                request.contentEditingOutput = output
                
            } completionHandler: { success, error in
                completionHandler(success, error)
            }
        }
    }
}

なんとかしたい

renderedContentURLに吐き出せるのがなぜかjpg一択？