Why ttf fonts become otf missing status, can it be solved by one click?

Most of the time, Font families (fonts with the same family name) are differentiated by type.

A few InDesign versions ago the types were even shown as icons in the Find Fonts dialog, now you have to use "More Info".

Lesser known, there are multiple "OpenType" types, showing the same [otf] suffix and the same icon, but they have a different type for matching. In scripting you can see them:

For this reason (types are relevant) you can come across multiple font families with the same family name, which is already known as bad and confusing the font subsystem thus better avoided, and even multiple [otf] of them. There are some more reasons for mismatches in font family - such as native names (discussed below).

This is the easy part. Under certain circumstances a font is identified by postscript name rather than by combination of font family, type and font style. Could be the placed PDFs where name+style are lost, or a copy-paste from Illustrator, where only the postscript name is known. When you import Word texts, they can also specify fonts never known to your system, I haven't looked what exactly happens then.

Anyway in these cases InDesign tries to substitute (one of the multiple font status values). Most of the time with Latin fonts it ends up at the default font (Myriad) but there is also a mechanism to list font families with "same name", and the found font might spill over. For inconsistency sake, dependent on the program one approach is taken or the other. For example a glyph might be found by the more forgiving composer and rendered accordingly a decade later from composer output, but the missing font highlighter might disagree.

The font lookup mechanism also differentiates between font managers - a font is less likely to get found with the document fonts folder even when it should along the mechanisms mentioned above, so sometimes it is suggested here in the forum to avoid document fonts.

Other criteria come with the font style, e.g. when you have the correct Arial around but the particular semi-bold is only in the other Arial … A font style might also spill over, within the family or across types, e.g. you specify Italic and get Kursiv, Regular for Roman. There is another mechanism that matches beyond the style name, and so forth.

All of these could explain why a Arial TTF specified in a legacy document could end up showing one Arial OTF that might happen to exist on your machine, even if you never used the OTF and the [Regular] font style is or isn't supported by the OTF font family.

Back to your screenshot - could be the paragraph style editor - which is also adding to the confusion. For example when you choose a named font style for a variable font, the font style name will display different from the font menu.

Font families and styles can also have multiple native names, displayed according to the system script if it is not Latin. Not sure why you show a pstyle with that GBK font while the question is about Arial, is that the chinese native name for Arial? If so, could be there is a mismatch in native name between the original Arial and your current one?

Otherwise, was Arial substituted in that pstyle and we're seeing the result? Both font family and font style are surrounded by [], which to me indicates something is missing for both. As we don't see the language from the following dialog page, and GBK is about a specific character set, maybe you have a mismatch there, and the language setting forced the GBK font?

I don't know enough about CJK typography, also for lack of example documents, so forgive any speculation errors.