Embedded css - is there any equivalent for the below implementation of css into Bokeh?

css = '''
.widget-box {
  background: #f02253;
}
'''

pn.extension(raw_css=[css])

There is not currently any API to inject CSS styles in to Bokeh output (only to set CSS classes). Two possibilities:

• Some folks have embedded <style> tags in Bokeh Div objects, which seems can work at least in some situations

• Add stylesheets to a custom Jinja template, and use the various bokeh.embed APIs to place plots, etc in the template.

Seems I have to use Jinja template then.
BTW
Does it exist any method/function to update the whole website when any change (i.e. in css) during app execution is made? similar to curdoc().add_periodic_callback

Bokeh does not monitor CSS for changes. Presumably you could make something work yourself with a MutationObserver (but I haven’t every tried so all I can do is suggest the possibility).