Does Verizon charge for call forwarding?
No. Not to a domestic number.
Fi charges $0.20/min for voice calls when traveling internationally. If you are receiving/making calls from/to the US while traveling internationally your best bet is to get a free Google Voice number and install the Google Voice app, and forward your US phone number to the Google Voice number. For Verizon, enable call forwarding using *72 + your GV number
before you leave for your trip. In the Google Voice app tell it to prefer data/Wi-Fi calling instead of voice minutes. Google Voice will then use VoIP for phone calls to/from the US which is free using your data plan (uses a tiny bit of data). You'll still pay Google Fi for international data service but this way you aren't paying per minute for voice. The only downside is when you call the US from Google Voice it will show as your Google Voice number and not your Verizon number. You can block your GV caller ID number though.
Google Fi works great but it's not cheap ($65/mo or $20/mo+$10/GB). Try a data-only eSIM provider like Airalo ($20 for 10GB, good for 30 days. Less if you need less data) together with Google Voice as mentioned above. You'll need a different eSIM for Europe and a different one for Israel though. Plus you won't have the ability to make local calls in the country you are visiting (though you could deposit money into Google Voice and use it to make calls to Europe and Israel at $0.01-$0.03/min).