Dear Shuyukh,
الجواب وبالله التوفيق
Regarding sunnah for fajr salah and sunan al-muakkadah while traveling, there are different scenarios with specific details.
The first scenario is while traveling, before reaching ones destination, during which one is in hurry, composure and calm are absent. The fuqahah have considered this state as sair. The second scenario is when the person has reached their destination and is now in a state of composure and calmness, fuqahah have considered that situation as nuzool.
In the first situation, with the exception of the sunnah for fajr, it is permissible to not read the sunnah for other salats, therefore one should not read them. In the second situation i.e. the state of calmness, it is best and preferred, to not only read the sunnah of fajr but to also read the sunnah for other salats, regardless of the location (i.e. harumor elsewhere).
عن البراء بن عازبؓقال صحبت رسول اللہ علیہ وسلم ثمانیۃ عشر سفرا، فما رائیتہ ترک الرکعتین قبل الظھر
(کتاب النوازل ، ص 455، ج 5، بحوالہ سنن الترمذی)
It has been documented from reference with Shami:
ویاتی المسافر بالسنن فی حال اوقرار والا بان کان فی خوف و فرار لا یاتی بھا ھو المختار لانہ ترک لعذر (کتاب النوازل ، ص 455، ج5
واللہ اعلم بالصواب