When Binance support replied to me, they asked me for my account uid, but I have a screenshot of the uid number. I gave them screenshots when I was withdrawing; if I hadn't had those screenshots, I probably wouldn't have been able to open my account, but somehow the screenshot as evidence helped.
Do you know that by giving a screenshot of your UID, you are creating more issues?
Like support will have to spend time to type your UID than just copy and paste it that is more easily.
Typing it manually from looking at your screenshot can cause typo and inaccuracy too.
For things you give in text, do it in text, don't do it in screenshot.
For your withdrawal history, you can go back to your email and forward Binance emails to you for your past withdrawals or you can regularly export your withdrawal history and save it.
Each person may have their own habits. There are those who regularly download historical data, there are also those who take screenshots. The aim remains the same, namely to make backups which will be useful for them when problems occur with their account or on the exchange where they put money for trading.
As long as it has a positive aim, why not? However, please note that there are some exchanges that don't provide historical data downloads, so maybe screenshots are another way to backup, or there are some traders who don't know about the history data download feature so they choose screenshots.