Is there a website with a list of all commercial airline incidents?
Each jurisdiction or organization will have its own reporting system, not all will provide that information to the public. News, social media, and websites provide information but more research is required to determine which parts are accurate.
https://aviation-safety.net/
The Aviation Safety Network is probably your best bet for both completeness and accuracy. The database is fairly comprehensive, contains events as far back as 1919, and lists sources. You can browse by date, location, and aircraft type. The Wikibase allows users to add incidents, providing coverage of many more small aircraft incidents but may be less accurate.
https://avherald.com/
Avherald strives for accuracy but is far from complete. Information is not reported without reasonable verification, sources are provided when possible. The team sometimes even has access to the radar data to provide more insight. Many news outlets use this as a source. Entries go as far back as 1999, but the items are intended to provide information on accidents and an overview of the types of incidents occurring worldwide. This will make any statistical analysis hard.
https://www.aeroinside.com/
AeroInside appears to just copy from Avherald and put the entries in a fancier format with ads and make them a bit more searchable.