Shaving of the head (halq) is recommended but not compulsory, therefore if a person has had a haircut (Taksir), his umra/hajj will also be valid.

Quran mentions both these things:

لَقَدۡ صَدَقَ اللّٰہُ رَسُوۡلَہُ الرُّءۡیَا بِالۡحَقِّ ۚ لَتَدۡخُلُنَّ الۡمَسۡجِدَ الۡحَرَامَ اِنۡ شَآءَ اللّٰہُ اٰمِنِیۡنَ ۙ مُحَلِّقِیۡنَ رُءُوۡسَکُمۡ وَ مُقَصِّرِیۡنَ ۙ لَا تَخَافُوۡنَ ؕ فَعَلِمَ مَا لَمۡ تَعۡلَمُوۡا فَجَعَلَ مِنۡ دُوۡنِ ذٰلِکَ فَتۡحًا قَرِیۡبًا

“[So, rest assured O Believers!] it is a fact that God had shown His messenger an absolutely true dream. Indeed, if God wills, you will definitely enter the Sacred Mosque with complete peace in a way that you will shave your heads and have hair-cuts; you will have no fear. It was only that God knew what you did not; so, before this, He blessed you with a victory near at hand“.

(Quran 48:27)

(Excerpt from Al-Bayan: Javed Ahmed Ghamidi)

(English Rendering by Dr. Shehzad Saleem)

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On the occasion of the final hajj, the Prophet (sws) himself had his head shaved (halq) and some of the Companions (rta) also preferred it (https://sunnah.com/bukhari:1729). Abu Huraira (rta) narrates that the Prophet (sws) prayed three times for those who had shaved their heads and once for those who had haircuts (https://sunnah.com/bukhari:1728).

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Please also refer to the video below from 14:05 to 15:00

https://youtu.be/RAFM2KvU32U?t=845