who can see my private browser history?

Wrong. From support.mozilla.org/en-US/kb/common-myths-about-private-browsing?as=u&utm_source=inproduct#w_what-to-know <blockquote>What to know '''Private Windows help keep your browsing private from others who use this device.''' They don't make you anonymous online or clear all of your data. Some activity in Private Windows may still be viewed '''by sites, search engines, internet providers, or your employer (if you’re on a work/school''' network or computer). A Private Window doesn't make you anonymous online. It doesn't hide your IP address or your location. </blockquote> So you'll leave breadcrumbs in services where you sign in using the same account as elsewhere. If a member of the household logs traffic on your networking equipment, they might be able to see the connection metadata, no matter whether private tabs or otherwise, as they are necessary for establishing the connections. And if e.g. your government requires your internet provider to keep a log, no matter which browsing mode you use — the traffic on the ISP side has no notion whether it originates from Private Browsing or not, they can have that. You'd need to use separate features to mask your traffic from your infrastructure vendors (several are available in Firefox). So the question is who you need to hide the browsing from.