hendi is right. It's an incandescent. Despite the bum advice you were given at the store and the fact that the thing is apparently sold as a "plant light" you can't grow plants under incandescent lights. As you have already seen, they give off too much heat. If it is close enough to do any good, it burns the plants. If it is far enough away, they get leggy. You would have been fine with the fluorescent tube you picked originally.
According to this map: https://www.plantmaps.com/interactive-wa ... te-map.php
, your first frost date in fall isn't until Nov, which sounds like a very long growing season (as would be expected in zone
. But maybe you weren't talking about freezing, just about cool and damp and not enough sun?
Cucumbers I would re-start. They are quick to germinate and quick to grow and they can't go in the ground until the soil is well warmed, so you have time to start over with cucumber seeds.
The tomato seedlings, if they are just leggy should be fine. Pinch off the seed leaves and re-pot the plants buried up to just below the first true leaves. They will root all along the buried stem and do well.
The peppers, you may just want to buy started plants this year. They are the slowest to germinate, slowest to grow and produce. They don't respond very well to the bury the stems trick. I plant pepper seeds the beginning of Feb and may not harvest my first peppers until July.
Sorry you got duped like that!