Looks like zone 1 traic is damaged. It’s fairly easy to replace with a soldering iron. Of course if you have a hot air gun that’s the best to replace surface mount components. If you don’t have a hot air gun, you can use a diagonal cutter to carefully cut the three legs on the right hand side, then use a soldering iron to remove each leg and the main body. The solder a new triac.
The replacement parts you ordered are fine. In particular, the triac is BT1308W. A suitable substitute is Z0103MN. It’s also possible to solder a through-hole version (MAC97A6 or MAC97A8 are both suitable substitutes) — just have to figure out the correct corresponding pins and solder through-hole legs to the surface mount pads.