I live in rainy SW Florida, and over the last 8-10 years have seen and talked to owners of three ebikes disabled due to water intrusion.
Yes, you need to take precautions.
If you have a throttle, you need a temporary cover as water intrusion is common here, and will disable the bike. No permanent damage, but no power till you dry it out. Have experienced this twice. Strip of small plastic grocery bag makes a good, temporary, disposable cover. Note that powered accessories on throttle body can make this far worse, I avoided those.
Controller ideally fully potted, otherwise drip loops in wires and consider adding drainage holes. Remember that everything you do to keep water OUT, will also act to keep water IN.
Most common serious problem area is charging port for battery. Often recessed allowing water to pool, covers provided not really adequate. Water intrusion can severely damage battery. Additional exterior cover which will also help hold the provided cover firmly in place recommended. Not having contacts at the bottom of a vertical channel also a good idea.
My bike has been strapped to the front of a bus doing 50mph thru monsoon-level rains for over 30 minutes, several times for shorter times, no problems. Throttle cover, drip loops, potted controller, waterproof sealed cover for charging port, waterproof battery housing.
BaFang mid-drives are IP65 "heavily water-resistant", and 500C controls are IP64. You don't want to submerge either but rain "splashing water" won't affect them. Batteries are batteries and are best kept inside the vehicle if traveling by car. I've been using a MAGT 130X thumb throttle for years now. In fact, I carried a spare in the bar bag for over two years just in case I ever needed it, and not long ago replace it in the middle of a ride... it wasn't raining at the time, I think it just wore out. There's another tucked into the bar bag right now and another in back-up. They're sold as "waterproof" but I can't find an IP rating and they certainly don't appear to be waterproof. But with over 24K miles on the old throttle while riding in the PNW is as waterproof as I have needed. If you drive around with your bike a lot it only takes a couple of minutes to pop it off the bike. I pull the side cases on the motor once a year and have never found any contamination or moisture. Little common sense and preventative maintenance works magic.
After putting the system all together i can see the wiring connections are sealed quite well. I did use some dielectric grease on the battery contacts and connection. Probably only a matter of time before i get caught out in a downpour. Will habe to cut some strips of plastic bag to protect the throttle as Nelson suggested. The rubber cover on my batterie's charge port fits tight and seems adequate.
The rubber cover on the batteries charge port was the part that failed on two of the three disabled ebikes I talked to owners on. The third had a vertical mount battery. I suspect those are relatively watertight with the battery in place, but when the battery is removed, not so much.
On the rubber cover, it is fairly easy to bump one out of the way, also they degrade over time and can get stiff, particularly when exposed to strong sun. It only needs to be partially on ONCE, when you get rained on.
My charge connector goes into a seperate, waterproof, vertical sleeve.
All wires run thru old 700c thin inner tubes used as conduit. Makes a perfect seal on the plastic nut cover over the hole in the axle.