The sun was shining bright this morning, but in the evening, it looked like it was about to rain, however, it didn't.

Now it is morning and the sun is shining bright, but in the evening it was supposed to rain. But it didn't rain.

This is morning, the sun was shining brightly but in the evening it was about to rain. But it didn't rain. The times are confusing me. When are you writing this? In the morning? The words "this is morning" indicate that you are writing in the morning. Which evening are you talking about? Today or last night? I would say "brightly" because "bright" is normally an adjective, and you need an adverb. I wouldn't call this a mistake because some people do use "bright" as an adverb, but I think "brightly" sounds more normal.

This morning, the sun was shining bright, but in the evening it looked like it was going to rain. But it didn't rain.

This morning and the sun was shining bright but in the evening it looked like it would rain. But it didn't rain.