How to make Telegram deep-linking work for messages?

I’m developing a bot, which creates games in Telegram.

When a user issues a /start_game command, the bot replies to user’s command with a message, which includes a link to the created game.

Now when the same user issues the /start_game command again, the bot responds with something along the lines:

Would you like to delete your currently active game and replace it with a new one?

The currently active game text should link to previously created game’s message via Telegram Deep Linking.

The way I do this currently is by using this deep link template from the docs:

f'<a href="tg://privatepost?channel={chat_id}&post={message_id}&single">{text}</a>'

Which worked fine under Telethon, but now that I switched over to Python-Telegram-Bot, it does not.

When clicked, such link says "Unfortunately you can’t access this message. You aren’t a member of the chat where it was posted.".

Well, I thought that the problem was because Telegram Bot API prefixes groups’ ids with - and channels’ ids with -100, so I got rid of those.

And now it says: "Message doesn’t exist".

Actual code:

def message_mention(text: str, chat_id: int, message_id: int, escape: EscapeType | None = 'html'):
    text = escape_string(text, escape)
    if chat_id is None or message_id is None:
        return text

    chat_id_string = str(chat_id)
    if chat_id_string.startswith('-100'):
        chat_id_string = chat_id_string[4:]
    elif chat_id_string.startswith('-'):
        chat_id_string = chat_id_string[1:]

    return f'<a href="tg://privatepost?channel={chat_id_string}&post={message_id}&single">{text}</a>'

What am I missing here?

The message_id must be correct, because later in the same function if the user clicked "Yes, delete the old game", it deletes the mentioned message fine and dandy.

UPD:

Minimal reproducible example, which attempts to link to a command just issued by the user.

async def main():
    from telegram import Update
    from telegram.ext import ContextTypes
    from telegram.ext import CommandHandler
    from telegram.ext import Application, Defaults


    app = (
        Application
        .builder()
        .defaults(
            Defaults(
                parse_mode="html"
            )
        )
        .token(BOT_TOKEN)
        .build()
    )

    def message_mention_lonami(text: str, chat_id: int, message_id: int):
        chat_id_string = str(chat_id)
        if chat_id_string.startswith('-100'):
            chat_id_string = chat_id_string[4:]
        elif chat_id_string.startswith('-'):
            chat_id_string = chat_id_string[1:]

        return f'<a href="https://t.me/c/{chat_id_string}/{message_id}">{text}</a>'

    def message_mention(text: str, chat_id: int, message_id: int):
        chat_id_string = str(chat_id)
        if chat_id_string.startswith('-100'):
            chat_id_string = chat_id_string[4:]
        elif chat_id_string.startswith('-'):
            chat_id_string = chat_id_string[1:]

        return f'<a href="tg://privatepost?channel={chat_id_string}&post={message_id}&single">{text}</a>'


    async def handler(update: Update, ctx: ContextTypes.DEFAULT_TYPE):
        chat_id = update.effective_chat.id
        message_id = update.effective_message.id

        mention1 = message_mention_lonami("Solution by lonami", chat_id=chat_id, message_id=message_id)
        mention2 = message_mention("Default solution", chat_id=chat_id, message_id=message_id)

        await ctx.bot.send_message(
            chat_id,
            "n".join([
                "is this your message?",
                mention1,
                mention2,
            ]),
        )

    app.add_handler(CommandHandler("test_mention", handler))

    async with app:
        try:
            await app.start()
            await app.updater.start_polling()
            await asyncio.Future()
        finally:
            await app.updater.stop()
            await app.stop()


if __name__ == '__main__':
    import asyncio
    asyncio.new_event_loop().run_until_complete(main())

Results in the client app: