No we don't include all those other things. Meaning, we don't include them in Alphabet books, in Alphabet songs, in the ASCII code ranges between a-z or A-Z. The Wikipedia page for "English Alphabet" starts [1] "The alphabet for Modern English is a Latin-script alphabet consisting of 26 letters". If you ask a random native school-educated English speaker to tell you the alphabet they will most likely tell you 26 letters and will not tell you diacritics that were used in older English writings to indicate the syllables. When you open a standard English dictionary there will be no section for words starting æ or wynn or &. If you put ö and é in a test of alphabet letters you would be marked wrong, even if you were then marked correct for writing "coöperation at the café", even if that's inconsistent.
You're nitpicking to try and score ackchually points, but it doesn't matter because everyone knows the English alphabet has 26 letters by some ratio like millions of speakers to 1.
That's because names aren't restricted to strings of English alphabet characters, not because there's any meaningful uncertainty about what characters the modern English alphabet contains.
OK:
1. Do we include the ampersand as last letter of the English alphabet? https://en.wikipedia.org/w/index.php?title=English_alphabet&...
2. Do we include arachaic letters? https://en.wikipedia.org/w/index.php?title=English_alphabet&...
3. Do we consider diacritic letters as own letters?
3a. Do we include diacritic letters that only appear in loanwords? https://en.wikipedia.org/w/index.php?title=English_alphabet&...
3b. Do we include diacritic letters that were used in older English writings to indicate the syllables? https://en.wikipedia.org/w/index.php?title=English_alphabet&...
3c. What about diacritics that appear in orthographies of regional dialects? https://en.wikipedia.org/w/index.php?title=English_terms_wit...
For 3, see also https://en.wikipedia.org/w/index.php?title=English_terms_wit...
4. What about ligatures that were in use in English until the 19th century, but are today much more rarely used? https://en.wikipedia.org/w/index.php?title=English_alphabet&...