I think the note was better as it was. Not confined to Buddhism - see the comments on the 冥福を祈る entry.

@@ -8,0 +9 @@
+<ke_inf>&sK;</ke_inf>
@@ -16,2 +17 @@
-<field>&Buddh;</field>
-<s_inf>人の〜. also 〜いたします, 〜申し上げます, etc.</s_inf>
+<s_inf>also 〜いたします, 〜申し上げます, etc.</s_inf>
@@ -19 +19 @@
-<gloss>I pray for your/his/her happiness in the afterlife</gloss>
+<gloss>I pray for your happiness in the afterlife</gloss>

Warning on being clear about the subject:
https://www.e-denpo.net/column/a045
ご遺族宛ての弔電の場合は、「〇〇さん（故人）のご冥福をお祈り致します」と記載するのがマナーです

https://www.yoriso.com/sogi/article/gomeifuku/
（故人に対して）
-May your soul rest in peace.（R.I.P.）
（遺族に対して）
-I’m sorry for your loss.
-I pray his/her soul may rest in peace.

http://officeclaro.blog46.fc2.com/blog-entry-278.html
・・関連表現・・
・彼女のご冥福をお祈りします。　May her soul rest in peace.
・ご冥福をお祈りします。　May your soul rest in peace.　

https://eow.alc.co.jp/search?q=冥福
（人）の冥福を祈る
mourn the loss of the lives of
offer one's sincerest prayer for the repose of someone's soul
pray for someone's happiness in the next world
pray for the repose of someone's soul
pray sincerely for the repose of someone's soul


https://cotoacademy.com/how-to-express-condolences-in-japan-guide-to-japanese-funeral/
3. Gomeifuku o oinori moushiagemasu ご冥福をお祈り申し上げます: May they rest in peace (in the afterlife)
“Gomeifuku wo oinori mou shiagemasu” is a prayer for the deceased’s soul meaning “May his/her soul rest in peace” or “I pray for his/her happiness in the afterlife”. The kanji 冥 means “dark” and is used in 冥土 (meido, the underworld), while 福 (fuku) means good fortune. Together, 冥福 (meifuku) means happiness in the afterlife.

It is normally used in condolence messages in Buddhist religion, so you need to be careful when using this phrase. It may be offensive if the deceased or bereaved family does not believe in the afterlife. It is best to avoid saying this if you are not sure of their religion.

https://buddha-and-me.blogspot.com/2012/12/does-buddhist-say-rest-in-peace.html?m=1
Does Buddhist say "rest in peace"?
Many people often say "rest in peace" ("RIP") when wishing someone who had died. It occurs to me that it is actually a quote with Christian origins, particularly Catholic... In Buddhism we do not rest in eternity or wait to be re-surrected by anyone. We continue into the next rebirth. Hence, as a Buddhist, it is more appropriate that we wish that the deceased will be reborn in the Buddha's Pure Land or reborn as a perfect human again or just a happy rebirth.
But it is just a small thing. It is not a big thing even if you say it because you are used to saying it. But I just want to clarify.

Comments and refs on 安らかに眠れ. 冥福 appears to be a Buddhist expression, which would explain the prevalence of this term in Japanese (vs. 安らかに眠れ in particular).

I feel like "rest in peace" is a western gloss of convenience which accurately communicates "condolences for someone's parting", but is quite disconnected with what this expression actually implies. (rebirth seems like quite the opposite of "rest").  But I guess it's just so common that it is what it is.

Note the warning: "It is normally used in condolence messages in Buddhist religion, so you need to be careful when using this phrase. It may be offensive if the deceased or bereaved family does not believe in the afterlife. It is best to avoid saying this if you are not sure of their religion."

Another warning I saw (and which alc seems to explicitly confirm): You should be careful about addressing this *at* the deceased, or otherwise specify whose soul you're praying for (not the listener): 〇〇さんのご冥福をお祈りします。  This may only be a minor social faux-pas that is not always observed. (But ideally you don't want to say "I pray for *your* soul in the afterlife" to the family of the deceased).  Changed from "may their soul" to "may your soul" to reflect this default. (I agree, it seems like context should make clear... but I read the warning)

On the death of a cast member of the popular netflix real-life drama:
https://www.instagram.com/p/CAieuggFPRt/?utm_source=ig_embed&ig_rid=44b069af-f4bd-4c73-a8cf-eab104870a4d
ご冥福をお祈りします。
Rest in paradise Hana (addressed *at* the deceased, as in English)

@@ -15,2 +15,5 @@
-<s_inf>also 〜いたします, 〜申し上げます, etc.</s_inf>
-<gloss>may their soul rest in peace</gloss>
+<xref type="see" seq="2840221">冥福を祈る</xref>
+<field>&Buddh;</field>
+<s_inf>人の〜. also 〜いたします, 〜申し上げます, etc.</s_inf>
+<gloss>may your soul rest in peace</gloss>
+<gloss>I pray for your/his/her happiness in the afterlife</gloss>

ご冥福をお祈りします	203480	95.5%
御冥福をお祈りします	9479	4.5%

Saw 御 on twitter in the wild first. Not surprising given how formal this is.

@@ -5,0 +6,3 @@
+</k_ele>
+<k_ele>
+<keb>御冥福をお祈りします</keb>

Nvm.

@@ -12 +12 @@
-<s_inf>also 〜をいたします, 〜を申し上げます, etc.</s_inf>
+<s_inf>also 〜いたします, 〜申し上げます, etc.</s_inf>

I think this is maybe clearer?

@@ -12 +12 @@
-<s_inf>also 〜いたします, 〜申し上げ, etc.</s_inf>
+<s_inf>also 〜をいたします, 〜を申し上げます, etc.</s_inf>