For text frame setup, you can use the Text panel's Text Frame section and options available via Expand.
Although the Frame Text Tool's context toolbar lets you format your frame text you use the Text panel to set the text frame stroke/fill color, insets, number of frame columns, irregular column and gutter widths, column rules, as well as vertical alignment control and a baseline grid.
Publisher will remember the last applied frame settings for new text frames.
Note that each frame retains its own independent frame properties. As a result, you can edit any selected text frame to change its setup just for that frame.
You can copy and paste text frame setups from a source text frame to one or more selected target text frames and also save any text frame as an asset in the Assets panel to a custom category, e.g. MyTextFrames.