Trying to connect to an uWSGI (or any other) server, from Solaris, will fail with the following error:

-bash-3.00# /opt/opsware/agent/bin/python3 client.py 
/tmp/client.py:9: DeprecationWarning: ssl.PROTOCOL_TLS is deprecated
  context = ssl.SSLContext(ssl.PROTOCOL_TLS)
Exception in thread Thread-1 (make_connection):
Traceback (most recent call last):
  File "/opt/opsware/agent/lib/python3.10/threading.py", line 1009, in _bootstrap_inner
    self.run()
  File "/opt/opsware/agent/lib/python3.10/threading.py", line 946, in run
    self._target(*self._args, **self._kwargs)
  File "/tmp/client.py", line 13, in make_connection
    with context.wrap_socket(sock, server_hostname=hostname) as ssock:
  File "/opt/opsware/agent/lib/python3.10/ssl.py", line 512, in wrap_socket
    return self.sslsocket_class._create(
  File "/opt/opsware/agent/lib/python3.10/ssl.py", line 1070, in _create
    self.do_handshake()
  File "/opt/opsware/agent/lib/python3.10/ssl.py", line 1341, in do_handshake
    self._sslobj.do_handshake()
BlockingIOError: [Errno 11] Resource temporarily unavailable

I used the following client code (based on https://docs.python.org/3.10/library/ssl.html#socket-creation):

import socket
import ssl
import threading

hostname = '192.168.135.9'
port = 1004

def make_connection():
	context = ssl.SSLContext(ssl.PROTOCOL_TLS)

	with socket.create_connection((hostname, port)) as sock:
		sock.settimeout(300) # use non-blocking I/O
		with context.wrap_socket(sock, server_hostname=hostname) as ssock:
			print(ssock.version())


t=threading.Thread(target=make_connection)
t.start()
t.join()

This works fine on multiple Linux distros, AIX, and HP-UX. It even seems to work on Solaris Sparc. There seems to be an issue only on Solaris (5.10/5.11) x86.
Furthermore, in order to reproduce the issue, the SSL handshake needs to be performed from a thread and use non-blocking I/O. If I use blocking I/O or don't use thread, the issue doesn't reproduce anymore.

The issues first started to appear in python 3.8.5 when I switched from openssl 1.0.2u to 1.1.1k. The issue is still reproducible with python 3.10 and openssl 3.0.0

Thanks for the detailed bug report.

Since the code works on Linux and other platforms as well as OpenSSL 1.0.2, it is likely a platform bug or a platform-specific issue with OpenSSL. Unfortunately I don't know how to investigate this issue.