No, that's not the case. If you buy FSD upfront you get free computer upgrades (which likely applies to HW4 also when it comes out). The people who have to shell out $1500 are older buyers with HW2.5 that did not buy the FSD option, but want access to the $200 per month subscription.
If all you want are the features show in FSD Beta, it'll likely be fine with HW3. And even if not, precedent has shown Tesla will retrofit whatever hardware necessary if you spend that $10k.
I had a FSD trial for 3 months and it does stop for traffic lights (you'll also need to confirm for greens for it to drive past them). There's more details here, but you should check your order page, which has the most up to date info on which of the features your car actually includes (I suggest taking screen shots as Tesla may change things).
Autopilot and Full Self-Driving Capability
You should also check out the manual page 99 (for traffic light feature, but other features are also described in other pages):
https://www.tesla.com/sites/default/files/model_y_owners_manual_north_america_en.pdf