In a procedure, when describing a UI component, we use the bold font to represent UI components. We also match the text with the letter case of the UI component. But do we need to match the font style too? For example, if the UI component is in italic formatting, do we need to write the text in italic characters?
This is all about recognition. The user may recognize the component being mentioned by name (verbal) or by sight (visual). Recognition by name is sufficient in most cases.
If you are going for recognition by name, the the reason for bolding the text in the manual is to offset the name from the rest of the text so that the reader can easily pick out the name. It is not about making the text look like the text in the interface, because you are relying on recognition by name, not appearance.
On the other hand, if you are going for recognition by sight, then you are creating a picture of the control in the documentation and that picture should be an exact match for the control or the visual match will not work. This means that you are going to want to match everything: font, color, style, etc. Often the best way to do this is with a graphic or a photograph of the control rather than by manipulating the font.
There is no point in doing anything between these two, however. If the visual match is not complete than either the reader's visual matching will be confused or they will fall back on verbal matching, in which case the font choice etc is irrelevant.
These are style questions and mostly a matter of opinion; but if the matching is intended to help the user recognize the key, then if I were writing a manual I would match the italics, and if possible the font as well.
I presume by "procedure" you do not mean code, but a recipe of action for a human operator to accomplish some goal or outcome.
Typically in documentation you would want every UI reference to be styled consistently. This would lead me to think that matching font styles to individual elements is not the ideal approach.
Best practice would be to create a style guide that includes how you are going to indicate a UI element, and adhere to that in all cases. This will help your audience recognize a UI element when they see one in the text.