Send hello and login asynchronously to speed up connecting

[bdraco]

Current we send HelloRequest, wait for a response, than send ConnectRequest and wait for a response.

We can send the HelloRequest and ConnectRequest, and than wait for both responses instead as it reduces one round trip wait.

This should speed up connecting with encryption enabled a little bit since it reported to be slow in home-assistant/core#103517 (comment)

INFO Starting log output from largegarage.local using esphome API
INFO Successfully connected to largegarage in 0.061s
INFO Successful handshake with largegarage in 0.022s
[18:45:21][I][app:102]: ESPHome version 2023.11.0b2 compiled on Nov  8 2023, 23:13:11

INFO Starting log output from icemaker.local using esphome API
INFO Successfully connected to icemaker in 0.020s
INFO Successful handshake with icemaker in 0.045s
[18:46:15][I][app:102]: ESPHome version 2023.12.0-dev compiled on Nov  9 2023, 16:50:08

[codecov]

Codecov Report

Merging #628 (76e2606) into main (8678fa9) will increase coverage by 0.55%.
The diff coverage is 86.36%.

@@            Coverage Diff             @@
##             main     #628      +/-   ##
==========================================
+ Coverage   77.93%   78.49%   +0.55%     
==========================================
  Files          14       14              
  Lines        2493     2511      +18     
==========================================
+ Hits         1943     1971      +28     
+ Misses        550      540      -10     

Files	Coverage Δ
aioesphomeapi/connection.py	85.34% <100.00%> (+2.81%)	⬆️
aioesphomeapi/reconnect_logic.py	88.65% <100.00%> (+0.36%)	⬆️
aioesphomeapi/client.py	53.96% <14.28%> (ø)

📣 Codecov offers a browser extension for seamless coverage viewing on GitHub. Try it in Chrome or Firefox today!

[bdraco]

Looks like we have no coverage for wrong password

[bdraco]

Manually test with wrong encryption key as well to make sure it doesn't cause a problem