You're going to have to provide a better example than that. For delete you are seemingly not correct.

https://github.com/reedy/AutoWikiBrowser/blob/master/AWB/Main.cs#L2550

For deletion it does check the rights a user has, not that they are a sysop

TheSession.User.CanDeletePage(TheSession.Page)

CanDeletePage - https://github.com/reedy/AutoWikiBrowser/blob/39e89bf1b805ee1f985f3854b414f52298b7e729/WikiFunctions/API/UserInfo.cs#L120-L123

public bool CanDeletePage(PageInfo page)
{
    return (HasRight("delete"));
}

Which calls HasRight https://github.com/reedy/AutoWikiBrowser/blob/39e89bf1b805ee1f985f3854b414f52298b7e729/WikiFunctions/API/UserInfo.cs#L98-L101

public bool HasRight(string right)
{
    return string.IsNullOrEmpty(right) || Rights.Contains(right);
}

Which checks that the user has the right listed...

For Protect, it looks like you might be, and that is easily fixed

btnProtect.Enabled = TheSession.IsSysop && btnSave.Enabled && (TheArticle != null);

OK, I will not argue, for deletion it was right in 2012, when I was closer.

But for editing protected pages, you don't understand me. I doesn't want to protect page using AWB button (I have no rights for this), I want (and can from browser, but not under AWB) to edit sysop-protected pages and MediaWiki namespace. I'm "engineer" in ruwiki, me (and my bot) has technical rights editinterface / editprotected / editsitejson, but when I try to edit such pages in AWB, I got an error "Page is protected".

In T260344#6383294, @MBH wrote:

But for editing protected pages, you don't understand me. I doesn't want to protect page using AWB button (I have no rights for this), I want (and can from browser, but not under AWB) to edit sysop-protected pages and MediaWiki namespace. I'm "engineer" in ruwiki, me (and my bot) has technical rights editinterface / editprotected / editsitejson, but when I try to edit such pages in AWB, I got an error "Page is protected".

If I don't understand you, it's because you've explained it poorly. You've mixed in various examples in one go, and seemingly made various assumptions, so it's hard to follow.

And most of your intial post is still wrong. AWB gets a list of the users rights from the API for years, and uses it for many actions

You get an error where?

https://github.com/reedy/AutoWikiBrowser/blob/fe2c9e12a4cb019b30822e2ac5be50bb6518e548/AWB/Main.cs#L1372-L1375

if (!TheSession.User.CanEditPage(TheSession.Page))
{
    SkipPage("Page is protected");
    return true;
}

which then calls

https://github.com/reedy/AutoWikiBrowser/blob/39e89bf1b805ee1f985f3854b414f52298b7e729/WikiFunctions/API/UserInfo.cs#L108-L112

public bool CanEditPage(PageInfo page)
{
    return (IsInGroup(page.EditProtection) || HasRight(page.EditProtection)) 
        && !(page.NamespaceID == Namespace.MediaWiki && !HasRight("editinterface"));
}

MediaWiki's editing rights etc have become more complex over the years, there's definitely numerous cases that probably aren't catered for.

Can you provide an example of which these pages are?

@Reedy see https://ru.wikipedia.org/w/index.php?title=Project:Википедия_не_даёт_медицинских_советов&diff=108714729&oldid=94916985 , but

My case:
I am an engineer and interface administrator at ruwiki, I have the editprotected right from the "engineer" user group.

I have tried to edit:

• https://ru.wikipedia.org/wiki/Template:France-geo-stub — a protected template
• https://ru.wikipedia.org/wiki/User:JWBTH/common.js — an other user's JS
• https://ru.wikipedia.org/wiki/MediaWiki:Gadget-convenientDiscussions — a system message

Only the last two were successful. Logs:

To be sure, for that test, I checked all the "Grant right" boxes in Special:BotPasswords.