This issue appears to date back at least 17 years (I didn't think Thunderbird was even that old), documented in various bug reports, and confirmed two years ago (and apparently now, with your question). For example, see Bugzilla:
There a various aspects to the problem:
1. Sending a plain text message which includes tabs works.
Tabs are shown 8 spaces wide in the compose window.
They are contained in the sent message and in the received message.
2. When viewing a plain text format=flowed message that contains tabs,
tabs are replaced with four spaces for display destroying any alignment.
<link now dead>
If preference mailnews.display.disable_format_flowed_support is set, tabs are displayed as tabs in flowed messages. Non-flowed messages already show tabs.
In the source view, which is essentially a giant <pre> block, tabs are shown
4 spaces wide.
Six years ago, someone confirmed (MozillaZine), that this was hard-coded, meaning that Thunderbird code would need to be modified and recompiled to fix it. The two links they cited are now dead.
I couldn't find any evidence that this has been fixed in Thunderbird, nor any reference to a preference setting for adjusting it, which would indicate that the problem still survives and there isn't a native fix for it.
It looks like fixing this in plain text messages will still require manual intervention, although it seems like the kind of thing that could be semi-automated via tab replacement. Given the history, this would seem like something somebody would have dealt with in an add-on, but I couldn't find one.
