Speed dial suggestions are speed dials automatically added to the start page below your regular speed dials. They're based on the sites you frequently visit. They can be hidden by disabling "Show Speed Dial suggestions" at the URL opera://settings/startPage.
However, there can be promotional speeds dials mixed in with your regular dials. Opera comes with some of those promotional ones by default. But, Opera might add/remove/change some of those promotional dials depending on the deals with companies Opera has at the moment. For promotional speed dials, you can move them to the trash, goto the URL opera://bookmarks and empty the bookmarks trash.
To stop new promotional speed dials from showing up, you can disable "Receive promotional Speed Dials, bookmarks and campaigns" at the URL opera://settings/privacy to see if it helps. There's also a "Display promotional notifications" option there too that you can disable.
At the URL opera://settings/startPage, you can also disable the 2 "continue shopping" options. Those can add a shopping section above your regular speed dials.
At the URL opera://settings/privacy/consentFlow, you can disable all 4 ad options.
For anything else on the start page, you can click the 'x' next to it and choose "don't show again".