Your anticipated departure date is 13 August. Even if your passport were unambiguously expiring on 13 November, you would be able to make the trip, because 13 November is the last day of validity, and 13 November is three months after 13 August.
The potential problem here is that as of 13 November 2023, the issue date of 13 November 2013 is arguably not "within the previous 10 years," meaning that your passport could be seen as having an effective expiration of 12 November 2023.
The Practical Handbook for Border Guards, however, very explicitly says that the ten-year requirement need only be met at the time of entry (page 28 of the 2022 version):
CHECKS ON THIRD-COUNTRY NATIONALS UPON ENTRY
3.1. The entry conditions to be fulfilled by third-country nationals when entering the
territory of a Schengen State are the following:
(a) the possession of a valid travel document or documents authorising them to cross the
border, whereby its validity must extend at least three months after the intended date
of departure from the Schengen States (although in a justified case of emergency,
this obligation may be waived) and it must have been issued within the previous 10
years; the requirement that the travel document must have been issued within the
previous ten years must be fulfilled at the day of entry (but not necessarily during the
stay)58, provided that its validity extends until the end of the stay plus three months;
*Example:
A third country traveller arrives on 21 November 2022 for a 20 days stay in the EU
with a passport issued on 23 November 2012 and valid until 23 March 2023. The
entry condition of Article 6(1), point (a), of the Schengen Borders Code is fulfilled,
since at the day of arrival the issuance date was less than 10 years ago and the
validity extends beyond three months after the intended date of departure.
(Emphasis added)