The THE BENJAMIN AND ROSE BERGER TORAH TO-GO Chanukah 5782 p 14 contains an article from Rabbi Ezra Schwartz entitled “ Al Hanisim in Birkat Hamazon”.
Tosafot, Shabbat 24a, s.v. Mahu, offer a different explanation. According to Tosafot, one needs to add Al HaNisim in tefilla since tefilla is held in public and there is pirsumei nisa. Benching, which is recited privately in one’s home, does not have a pirsumei nisa element to the same extent that tefilla does.
The text of the Tosfos reads
מהו להזכיר של חנוכה בבהמ"ז. בתפלה פשיטא ליה דמזכיר משום דתפלה בצבור הוא ואיכא פרסומי ניסא אבל בבהמ"ז שבבית ליכא פרסומי ניסא כולי האי:
What about mentioning Hanukkah in Grace after Meals. It's obvious that Hanukkah must be mentioned in communal prayer because there is the element of publicising the miracle but in Grace there is not so much publicity.
Rabbi Schwartz says further:
It seems that for Tosafot, even private prayer counts as pirsumei nisa. The conclusion of the Gemara that one can or perhaps should recite Al HaNisim in Birkat HaMazon, indicates for Tosafot that pirsumei nisa is not as it is commonly understood: a public declaration of the miracle. Instead, even a personal awareness of the neis can constitute pirsumei nisa. Pirsumei nisa is as much to oneself as it is to others.
פִּרְסֵם, פִּירְ׳ (enlargement of פָּרַס) to spread, divulge, publish; to uncover, expose.
How can I understand the idea that “Pirsumei nisa is as much to oneself as it is to others.”
related: Lighting Hanukkah Candles Alone