I'm creating text frames in Draw. I cannot use the "small capitals" font feature any more. All of the other font effects (capitals, lowercase, and titles) continue unaffected. Is there a bug in the application?

About the application: Version, Build 1:6.0.7 0ubuntu0.18.04.10, OS Linux 5.3.

Step 1: I am creating a document in Draw. Step 2: I create a text frame and select a font. Step 3: I highlight the text to be manipulated. Step 4: I go into “Character,” and click on “small capitals.” The preview box shows the letters the way they are supposed to appear. After I click “OK,” nothing happens. The highlighted letters are still in their original shapes. I test other fonts and the same thing happens with them. Do I have a bug in the application?

Here LO I get the “small capitals” effect. You can access the dialog either with Format>Character or a click on the “More Options” small icon (3 horizontal lines in my icon theme) in the style side pane. Both give the effect.

Are you both talking about something concerning Draw? I don’t know TextFrame objects there, but only TextBox shapes. Below I am talking of the behaviour of TextBox shapes.
In pursuit of this question I found more than one bug in V 5.4.4 and in V 6.4.0, but I couldn’t find the way @ajlittoz described. (I may have disabled some icons.)
I only can suggest to report to bugs@libreoffice.org.
Both versions I tested showed the wanted effect in the preview under
>Format>Character>Font Effects>Effects if Case: Small capitals was selected. The older version also showed it in the text box as long as the text was selected. Both of them didn’t show it any longer as soon as the text was unselected or the TextBox left.
Trying it with a TextBox (NOT a frame!) in Writer, 6.4.0 crashed reproducibly while 5.4.4 behaved the same way as described for Draw.

@Lupp: since OP tagged draw, I “translated” text frame into text box.

As long as some text is selected before applying style changes, it remains after leaving the box. Of course, if nothing is selected before, it applies only to the cursor location (a 0-character sequence) or to text immediately typed from there.

In case this is relevant: Fedora 31, LO from distro packages

Of course I selected the text before trying to “format” it. What I got was as already described. Currently I have no linux for testing, and also not any LibO V 6.3.y.
I just tried with a 32-bit 6.2.5 (on Win 10) in ‘Draw’ with a few different fonts and got the same behaviour as with V 6.4.0 - except the crash when testing with a TextBox shape in Writer.

Just also tested with V 64-bit on Win 10 with a virgin user profile. Observations as already described (but no crash).