I dug around more, ended up refactoring a bit of code took the liberty to push my changes to your branch. Managed to fix the nested entities stuff (and I'm wondering why the if offset == 0 never caused problems so far).

What's still missing is throwing an exception for two consequcitve block quotes in MarkdownV2.

Moreover, even though block quote parsing seems to be working correctly now, I think there is a bug on TG side. Sending a text of the form ">A\nB" leads to TG detecting a Message entity of length 2 instead of 1, which includes the "\n". You can reproduce this via

https://api.telegram.org/botTOKEN/sendMessage?chat_id=CHAT_ID&text=%3EA%0AB&parse_mode=MarkdownV2

If you try to compute the text_md_v2 for the resulting message, the B will be moved into the block quote.

For completeness, let me also share my renewed testing script:

Details

import asyncio
import json
from pathlib import Path
from pprint import pprint
from telegram import Message, Update, Bot
from telegram.constants import ParseMode
from telegram.ext import CallbackContext, Application, MessageHandler, filters
def get_message(bot: Bot) -> Message:
    return Update.de_json(json.loads(Path("response_3.json").read_bytes()), bot).effective_message
async def main():
    async with Bot("TOKEN") as bot:
        message = get_message(bot)
        await run_tests(message)
def get_formatted_text(message: Message, parse_mode: ParseMode) -> str:
    return getattr(message, f"text_{parse_mode.name.lower()}")
async def run_tests(message: Message) -> None:
    print(repr(message.text))
    pprint(repr(message.entities))
    for parse_mode in (ParseMode.HTML, ParseMode.MARKDOWN_V2):
        print("-" * 80)
        print(f"Replying with {parse_mode}:")
        await message.get_bot().send_message(
            chat_id=1145108092,
            text=f"============ Replying with {parse_mode}:",
        )
        formatted_text = get_formatted_text(message, parse_mode)
        print(repr(formatted_text))
        reply = await message.get_bot().send_message(
            chat_id=1145108092,
            text=formatted_text,
            parse_mode=parse_mode,
        )
        print(reply.text == message.text, repr(reply.text), repr(message.text), sep="\n")
        print(
            reply.entities == message.entities,
            repr(reply.entities),
            repr(message.entities),
            sep="\n",
        )
        pprint(reply.parse_entities())
        print(
            reply.text_html == message.text_html,
            repr(reply.text_html),
            repr(message.text_html),
            sep="\n",
        )
        print(
            reply.text_markdown_v2 == message.text_markdown_v2,
            (reply.text_markdown_v2),
            (message.text_markdown_v2),
            sep="\n====\n",
        )
        next_reply = await reply.reply_text(
            get_formatted_text(reply, parse_mode), parse_mode=parse_mode, quote=True
        )
        await next_reply.reply_text(
            get_formatted_text(next_reply, parse_mode), parse_mode=parse_mode, quote=True
        )
if __name__ == "__main__":
    asyncio.run(main())

response.json:

{
    "update_id": 219020534,
    "message": {
        "message_id": 31843,
        "from": {
            "id": 1145108092,
            "is_bot": false,
            "first_name": "Hinrich",
            "last_name": "Mahler (@Bibo-Joshi)",
            "username": "BiboJoshi",
            "language_code": "de"
        },
        "chat": {
            "id": 1145108092,
            "first_name": "Hinrich",
            "last_name": "Mahler (@Bibo-Joshi)",
            "username": "BiboJoshi",
            "type": "private"
        },
        "date": 1704553973,
        "text": "block \\n quote\nABC\nblock \\n quote\nwith \\n line break\nDEF\nblock \\n quote\nwith \\n line breakp",
        "entities": [
            {
                "offset": 0,
                "length": 14,
                "type": "blockquote"
            },
            {
                "offset": 9,
                "length": 5,
                "type": "underline"
            },
            {
                "offset": 19,
                "length": 33,
                "type": "blockquote"
            },
            {
                "offset": 28,
                "length": 5,
                "type": "italic"
            },
            {
                "offset": 28,
                "length": 5,
                "type": "strikethrough"
            },
            {
                "offset": 57,
                "length": 34,
                "type": "blockquote"
            },
            {
                "offset": 66,
                "length": 5,
                "type": "spoiler"
            }
        ]
    }
}