How to identify rhymes in a Tang poem?
In the character's zdic entry, there is a section labelled 音韻方言, which will have the character's rime group (韻目). In the 廣韻 section, 城 is labelled under the header 清. Ctext further has a more organised version of 廣韻, which you can quickly Ctrl+F your way into 清, which will list all the characters under that rime.

If you have some knowledge of other Chinese languages, or some understanding of how Sinoxenic vocabulary works in Japanese/Korean/Vietnamese, you can corroborate the fact that, at least in some non-Mandarin pronunciations, those characters that you listed did indeed rime.

Interestingly, 清 and 靑 did not rime in Guangyun, as evidenced by the fact that it had its own rime entry.