Hi
Based on my test in Power BI desktop version 2.40.4554.463, the TimeLine visual can be resized, it needn't to occupy lots of space. If the date bar is wider than the visual width, the horizontal scroll bar will generate automatically for us to drag horizontally to select different date ranges. See:
Also we can change the font size of date labels, see:
Best Regards,
Qiuyun Yu