Creating a Python Log-In system using text files

I'm trying to create a basic Sign-up and Sign-in system in python using text files. I also want the program to run in one go, meaning I want the user to be able to signup, and then proceed to log in right away, instead of having them go back and run the code again. The code that I have written though, can't do that for some reason. I've added "signin()" at the end of the sign up function to allow the users to proceed to sign in after a successful registration, but doing so throws an error. Instead I have to run the code again for the new signup to be recognized.

Here's the code:

def signin():
    q = 0
    user = input('Username: ')
    password = input('Password: ')
    with open('username.txt', mode='r')as names:
        for i in names:
            foundname = names.readlines()
    with open('password.txt', mode='r')as passwords:
        for j in passwords:
            foundpass = passwords.readlines()
    if user + "\n" in foundname:  # ReadLines() adds newlines
        user_num = foundname.index(user + "\n")
        for i in range (0,user_num):
            if password + "\n" == foundpass[i]:
                print("Login Successful.")
        print("Incorrect Password. Try Again.")
        signin()

    else:
        print("Username not found. Try again")
        signin()

def signup():
    with open('username.txt', mode='a')as names:
        print("Please provide the following details to sign up")
        name = str(input("Username: "))
        names.write(f"{name}\n")
    with open('password.txt', mode='a')as passwords:
        password = (input("Password: "))
        passwords.write(f'{password}\n')
        print("signup successful. You can sign-In Now.")
        signin()
signup()

Here's the output and the error I keep getting:

Please provide the following details to sign up
Username: abcdef
Password: password1
signup successful. You can sign-In Now.
Username: abcdef
Password: password1
Traceback (most recent call last):
  File "D:/student.py", line 34, in <module>
    signup()
  File "D:/student.py", line 33, in signup
    signin()
  File "D:student.py", line 14, in signin
    if password + "\n" == foundpass[i]:
IndexError: list index out of range

Process finished with exit code 1

But when I run the code again, the credentials I used to sign up the last time seem to work.

Please provide the following details to sign up
Username: jkl
Password: mno
signup successful. You can sign-In Now.
Username: abcdef
Password: password1
Login Successful.

Thanks a lot in advance!