@AceDude If I understand you correctly:
The Switch controls the Outlet to be switched on or off and you are using a std outlet but replacing the std switch with HS200 - and then plugging Lamp with Smart Bulb into the Outlet ........ yes?
So - the reason you have delay is that with the switch 'off' (and this would be the case whether a Smart Switch or a std wall switch) then the Smart Bulb has no Wifi radio active until after the outlet is switched on - then the bulb needs to re-establish that Wifi connection to your router.
You really cannot use a dimmer in this application - and even the Smart Switch is not really viable unless you just wanted to turn it on or off (without any dimming capability)
The part I'm confused about - the point of a Smart Switch is to be able to (predominantly) control it without physical action of the switch; BUt sounds like you also want that capability to be able to turn it on manually as you enter that room
I don't see that it's really possible to create a manual control of the dimming capability (unlike a permanent Ceiling Light FIxture - because you can't/shouldn't be using a dimmer to control an outlet - consider that ANY device could possibly plugged into that outlet by some unknowing person - potentially a much higher wattage device than a Smart Bulb!)
Would it 'work' with an HS220 and a regular dimmable (non-smart) LED in the lamp? Well yes .... however this is a very dangerous situation for the reason outlined. Imagine a Vacuum cleaner or similar being plugged into that Outlet!!
So please don't do that.
If you just want to be able to at least turn the lamp on/off with the physical switch (while setting the Smart Bulb Dimming intensity from the App) then here's what I would suggest:
1. Use an HS200
2. Use a Kasa Smart Bulb
3. Connect the Smart Switch to Line and Neutral HOWEVER connect the LOAD wire in the Switch Box (that goes to the Outlet) ALSO to the Line (so that the outlet is now always 'hot' and not being physically switched by the Smart Switch - or alternatively you can leave the load switched and just plug the Lamp into the non-switched receptacle) If you bypass the Load Wire directly to Line, then cap off the unconnected Line Output from the HS200 with a Wire Nut.
4. Set up an automation where powering 'on' the Smart Switch (whether physically or by App) Turns ON the Light Bulb and vice versa
Now the switch is not physically controlling the lamp - it is simply(?) creating a control command that is 'smartly' relayed to the lamp to turn it on or off.
This is what is known as an IFTTT control - IF This (happens) Then That (happens)
So the Switch is a Smart 'Dummy' - and in this case it really means Dummy, Not Dumb (which is a not-Smart Switch) since it does not physically switch a circuit but only creates a 'state' that can be used to control other devices (in this case the Lamp Smart Bulb)
You can do this by creating a 'Smart Action' in the Kasa App (or by using Alexa or Smart Things)
The action would be - when your Smart Switch turns on, turn on the Smart Bulb (to use the Kasa App you would need to have a Kasa Smart Bulb - for the other apps, any brand would work).
The delay should be much less because now the Smart Bulb is constantly powered (even if not illuminated) so the WiFi Radio is always active.
I don't really use the Kasa App myself - you might even be able to select a default intensity setting of the bulb to turn on to.
Hope that helps!
p.s. Looking at your orginal application - lamp controlled by switch near the door - you could even use a wireless contact sensor on the door and set up an automation that says IF Door Opens AND its between Sunset and Sunrise (or specifc times) THEN Turn on the Lamp :D
(Don't think you can do this in Kasa App though)