Should one say “Astagfirullāh” after offering Salam at the end of every different types of unit of prayer be it Sunnah or Farḍ and be it Tahajjud or the obligatory prayers and the Sunnahs associated with them?

Praise
be to Allah

Seeking
forgiveness (istighfaar) after the obligatory prayers is proven to be
something that the Prophet (blessings and peace of Allah be upon him) did,
because of the report narrated by Muslim (1362) from Thawbaan (may Allah be
pleased with him), who said: When he had finished his prayer, the Messenger
of Allah (blessings and peace of Allah be upon him) used to ask for
forgiveness three times and say: “Allaahumma
anta al-salaam wa minka al-salaam, tabaarakta yaa dhaa’l-jalaali wa’l-ikraam
(O Allaah, You are al-Salaam (the One Who is free from all defects and
deficiencies) and from You is all peace, blessed are You, Possessor of
majesty and honour).”

The view of the
majority of scholars is that this istighfaar and the praise of Allah that
follows it is only to be said after an obligatory prayer, so it is not to be
said after a naafil (supererogatory) prayer.

But there is a
du‘aa’ for seeking forgiveness (istghfaar) that is prescribed after all acts
of worship, in general terms.

Allah, may He be
exalted, has enjoined it after departing from Muzdalifah in Hajj, and after
praying qiyaam al-layl (voluntary night prayers), and the Sunnah indicates
that it is prescribed after doing wudoo’, after gatherings of dhikr (e.g.,
study circles), and in other circumstances.

It is a prayer
seeking forgiveness for falling short in doing the act of worship. Allah,
may He be exalted, says (interpretation of the meaning):


“… 
But when you depart from ‘Arafat, remember Allah at al- Mash‘ar al-Haram.
And remember Him, as He has guided you, for indeed, you were before that
among those astray.


Then depart from
the place from where [all] the people depart and ask forgiveness of Allah.
Indeed, Allah is Forgiving and Merciful”


[al-Baqarah
2:198-199].

Ibn Sa‘di said
in his commentary on this verse:

“Then depart from the place from where [all] the people
depart” i.e., then depart from Muzdalifah, from where all the people
have departed, from the time of Ibraaheem (peace be upon him) until the
present. What is meant by this departing was well-known to them; it meant
departing and stoning the jamaraat, offering the sacrifice, circumambulating
the Ka‘bah (tawaf), going between as-Safaa and al-Marwah (sa‘i), staying
overnight in Mina during the days of at-tashreeq, and completing all the
other rituals of Hajj.

Because the
purpose of this departing was as mentioned, and the things mentioned are the
last of the rituals of Hajj, Allah commanded that when finishing them, we
should ask Him for forgiveness and remember Him a great deal.

So forgiveness
is sought for mistakes made by the individual when doing his act of worship,
and for his shortcomings therein. Remembering Allah is thanking Allah for
the blessing that He bestowed upon him by enabling him to do this great act
of worship.

This is what the
individual should do: every time he finishes an act of worship, he should
ask Allah for forgiveness for his shortcomings, and thank Him for enabling
him to do it. This is unlike the one who thinks that he has done the act of
worship perfectly and has done a favour to his Lord by doing it, and that it
will give him high status. Such a one deserves to be despised (by his Lord)
and to have his deed rejected, just as the former deserves to be accepted
and enabled to do more good deeds.

End quote from
Tafseer as-Sa‘di (p. 92).

 Allah, may He
be glorified and exalted, praises those who focus on seeking forgiveness
after praying tahajjud, as He, may He be exalted, says (interpretation of
the meaning):


“They
used to sleep but little of the night,


And in the hours
before dawn they would ask forgiveness”


[adh-Dhaariyaat
51:17-18].

It was narrated
from Naafi‘, that Ibn ‘Umar used to spend the night in prayer, then he would
say: O Naafi‘, is dawn approaching? And he would say: No. So he would go
back and pray some more, then he would say: O Naafi‘, is dawn approaching?
And he would say: Yes. So he would sit and pray for forgiveness and offer
supplication until dawn broke.

It says in
Majma‘ az-Zawaa’id (9/346): It was narrated by at-Tabaraani and the men
of its isnad are the men of as-Saheeh, apart from Asad ibn Moosaa,
who is thiqah (trustworthy).

Al-Hasan
al-Basri said in his commentary on the passage, (interpretation of the
meaning): “They
used to sleep but little of the night, And in the hours before dawn they
would ask forgiveness”
[adh-Dhaariyaat 51:17-18]:

They would make
their prayer lengthy and pray with energy until, when dawn approached, they
would begin to pray for forgiveness.


Tafseer
at-Tabari
(21/510).

It is narrated
in a sound report from the Prophet (blessings and peace of Allah be upon
him) that he offered the supererogatory Duhaa [mid-morning] prayer, then he
followed it with istighfaar (prayer for forgiveness). It was narrated that
‘Aa’ishah (may Allah be pleased with her) said: The Messenger of Allah
(blessings and peace of Allah be upon him) prayed Duhaa, then he said: “Allaahumma’ghfir
li wa tubb ‘alayya, innaka anta at-Tawwaab ar-Raheem (O Allah, forgive
me and accept my repentance; verily You are the Acceptor of repentance, the
Most Merciful)”, and he repeated it one hundred times.

Narrated by
al-Bukhaari in al-Adab al-Mufrad (619) and an-Nasaa’i in as-Sunan
al-Kubra (9935); classed as saheeh by al-Albaani.

This was also
narrated via an Ansaari man, but ‘Aa’ishah did not name him. An-Nasaa’i
regarded this isnad as more likely to be sound, as he says in as-Sunan
al-Kubra (9/46). See: Tuhfat al-Ashraaf (11/398).

This offers
evidence from the actions of the Prophet (blessings and peace of Allah be
upon him) for this practice.

Something
similar was also narrated from ‘Umar ibn al-Khattaab (may Allah be pleased
with him), but its isnad is da‘eef. See: It-haaf al-Khiyarah al-Mahrah 
by al-Busayri, no. 1757; al-Mataalib al-‘Aaliyah by Ibn Hajar (644),
and the comments of the annotator.

And Allah knows
best.

Conclusion:

Seeking
forgiveness is prescribed, in general terms, after doing acts of worship,
because of the shortcomings that may occur. So there is nothing wrong with
seeking forgiveness after offering a naafil prayer, and there is no problem
if the wording is that of the usual prayer for forgiveness that is recited
after offering an obligatory prayer: by saying “Astaghfir Allah, astaghfir
Allah, astaghfir Allah” and so on; in fact that is preferable to other words
in this case.