ACROSS

 1 TIPSY TIP, “the point” + S and Y

 4 PSEUDONYM P{S}EUDON{Y}M, DUE, “expected”<=“back” + ON, “over” inside PM, “afternoon” with S and Y inserted

 9 SATYRIC A + TRIC[-k] with S and Y inserted

10 OUTSTAY Anagram (“dilapidated”) of “auto” with S and Y inserted

11 DROWSY WORD<=“retro” + S and Y

12 NEW STYLE NEWT, “Salamander” + L(ake) + E, “last of JunE” with S and Y inserted

14 SIMPLICITY {S}IMPLICIT{Y}

15 OA[-t] with S to start and Y inserted

18 SONY {S}ON{Y}, ON being “working”

19 POSITIVELY LEVI “Strauss” + T(I)OP, “PuccinI ultimately inserted in high point” <=“in retrospect” with S and Y inserted

21 EASTERLY Hidden in Greater London with S and Y inserted

23 SLEEPY PEEL, “skin”<=“seen in the mirror” flanked by S and Y

26 CAT’S EYE CATE, “Blanchett” + E, “beginning to Exhibit” with S and Y inserted

27 SYMPTOM S and Y then MP, “British politician” + (British actor) TOM “Holland”

28 SURVEY MAP U, “turn” + anagram (“flawed”) of REVAMP with S and Y inserted

29 SANDY S and Y

DOWN

 1 TASED T(AS)ED—That “Williams” is TED and “playing” is AS, as in “Christopher Reeve AS Superman“

 2 PATROLMAN Anagram (“ill-advised”) of “plan to arm”

 3 YARD SALE Anagram (“reorganized”) of “already” + S(alt)

 4 PICK Double definition

 5 EGOCENTRIC E(GO)(CENT)RIC

 6 DETEST Anagram (“tamed”) of “steed” + central letter of “wesTern”

 7 NUTTY Anagram (“decomposing”) of “Tut” inside N(ew) Y(ork)

 8 MAYBE BABY MAY, “Thirty-One Days” + B, “second-rate” + B, “alBum’s third [letter]” inside EBAY, “online auction site”

13 SCHOOL TERM Anagram (“Engineer”) of “colors the” + M, “western edge of Muslim”

14 SESTERCES “Crest” is a letter bank, its parts used and reused to make the answer

16 OVEREATEN Anagram (“Give order to”) of “a tenor Eve”

17 DIPLOMAS Anagram (“Cultivated”) of “damp soil”

20 SERENE SEREN[-AD]E

22 SITAR S(I)TAR, I being 1, “‘the first”

24 YUMMY Last letter (“finally”) of pastrY + UM, “er” + MY, “belonging to the author”

25 RSVP Even letters (“Nothing odd”) in “Irish VIP”