I hear your sentiments, @usernestor-ale.

I'd like to make it up to you by sharing some information about the class feature in QuickBooks Online.

First, you're correct that the assigned classes won't appear when there's a VAT code assigned to them. I appreciate your great ideas and recognize your need for this feature. 

In this case, I'd like to guide you on how to send feedback. This way, our developers can consider adding the said option in future product enhancements.

Here's how to send feedback:

1. Click the Gear icon at the top, and then choose Feedback.
2. Enter your comments or product suggestions, like "I'd like to see classes to transactions with VAT code assigned in QuickBooks Online."
3. You can also attach a photo to emphasize your concern, and then select Next.
   
4. Click Send message when you're ready.

For more details, please head to this link: How do I submit feedback?

With regards to the "detail report" that my peer mentioned, one example I can suggest is the Profit and Loss Detail report. You can run the report and filter it to show your desired class lists. I've included a screenshot for a visual guide:

Also, I'd agree that it's better if only one agent will assist your concern throughout. What I can do on my end is to take note and pass this brilliant suggestion to our managerial team. This way, we can add this as another method when replying here in the Community.

You're also right that a "bridge account" isn't necessary when recording transfers with the same currency. Otherwise, you'll need to add one to prevent errors.

Lastly, I recommend checking our QuickBooks Blog page from time to time. This way, you can keep up with the current news and product cascades.

Keep me posted if you need more QuickBooks tips or insights on managing your transactions. I'm here to help you anytime.