Open Links & blocks → Import, paste the public URL of your old page and press Find links.
Linky reads the public HTML of that page and lists every outgoing link with its title. Tick the ones you want and press Add. Links to the old service itself are skipped. Nothing is written until you choose, and nothing happens to the old page.
Icons are detected from the URL (Instagram, YouTube, and so on). Check titles and press Save.
If a service blocks automated reads, the import says could not reach that page; copy the links by hand in that case.