What's the best approach to avoid defining sqlite3 conn and cursor in many different functions?

A context manager: Create a context manager that handles the connection and cursor creation, as well as closing the connection when done. This way, you can use the with statement to manage the connection and cursor in your functions.

import sqlite3

DB_FILE = "your_database_file.db"

class DatabaseConnection:
    def __enter__(self):
        self.conn = sqlite3.connect(DB_FILE)
        self.cursor = self.conn.cursor()
        return self.cursor

    def __exit__(self, exc_type, exc_val, exc_tb):
        self.conn.commit()
        self.cursor.close()
        self.conn.close()

def insert_post_to_db(issue: Issue, lemmy_post_id: int) -> None:
    with DatabaseConnection() as cursor:
        cursor.execute(
            "INSERT INTO posts (issue_url, lemmy_post_id, issue_title, issue_body) VALUES (?, ?, ?, ?)",
            (issue.url, lemmy_post_id, issue.title, issue.formatted_body),
        )

A function decorator: You can create a decorator that handles the connection and cursor creation and passes the cursor to the decorated function.

import sqlite3
from functools import wraps

DB_FILE = "your_database_file.db"

def with_cursor(func):
    @wraps(func)
    def wrapper(*args, **kwargs):
        conn = sqlite3.connect(DB_FILE)
        cursor = conn.cursor()

        result = func(cursor, *args, **kwargs)

        conn.commit()
        cursor.close()
        conn.close()

        return result

    return wrapper

@with_cursor
def insert_post_to_db(cursor: sqlite3.Cursor, issue: Issue, lemmy_post_id: int) -> None:
    cursor.execute(
        "INSERT INTO posts (issue_url, lemmy_post_id, issue_title, issue_body) VALUES (?, ?, ?, ?)",
        (issue.url, lemmy_post_id, issue.title, issue.formatted_body),
    )

Have you thought about using an ORM?