[Quoth]

I'd never used Cntrl Shift U, as my keyboard map has all common and Compose has rarer (you can add to Compose). I did have an issue with aspects of Compose not working in QT and some programs. I have an .Xcompose but

include "/usr/share/X11/locale/en_US.UTF-8/Compose"

needed to be in the first line.
Suits all western Locales, there is none for other en_ as the whole point is that it adds all Latin/Roman/Western non-English characters, e.g. óþł§ßĸðç etc Compose ~ n gives ñ

Some of my Linux systems needed this executed in the Console/terminal/command line for QT applications to work properly.

im-config -n ibus

I disable Caps Lock, make Compose be Caps Lock and then both shift is CapsLock and either cancels.

I just tested Cntrl Shift U 256 Return in Calibre Editor: the main HTML edit window, find and replace boxes.
Shows u digits and then when return hit gives ɖ

Linux Mint 20.1, Mate Desktop, Server2003 theme, XP Metallic window frame and Window Manager = Marco +Compositing
(Marco +Compositing allows transparency so drag & drop in programs like Thunderbird lets you see text on destination folder)

My custom .XCompose in Home (~) has Greek via Compose g and Compose G, prime ′ and double prime ″ (feet, inches or minutes, seconds) using Compose 0 ' and Compose 0 "

I've not tried adding all the special spaces to Compose. At least one is on Space Bar. Alt Space is Title bar menu as in Windows.
.XCompose

Spoiler:

include "/usr/share/X11/locale/en_US.UTF-8/Compose"
# GREEK CAPITAL LETTERS
<Multi_key> <G> <A> : "Α" U0391 # GREEK CAPITAL LETTER ALPHA
<Multi_key> <G> <B> : "Β" U0392 # GREEK CAPITAL LETTER BETA
<Multi_key> <G> <G> : "Γ" U0393 # GREEK CAPITAL LETTER GAMMA
<Multi_key> <G> <D> : "Δ" U0394 # GREEK CAPITAL LETTER DELTA
<Multi_key> <G> <E> : "Ε" U0395 # GREEK CAPITAL LETTER EPSILON
<Multi_key> <G> <Z> : "Ζ" U0396 # GREEK CAPITAL LETTER ZETA
<Multi_key> <G> <H> : "Η" U0397 # GREEK CAPITAL LETTER ETA
<Multi_key> <G> <I> : "Ι" U0399 # GREEK CAPITAL LETTER IOTA
<Multi_key> <G> <K> : "Κ" U039A # GREEK CAPITAL LETTER KAPPA
<Multi_key> <G> <L> : "Λ" U039B # GREEK CAPITAL LETTER LAMDA
<Multi_key> <G> <M> : "Μ" U039C # GREEK CAPITAL LETTER MU
<Multi_key> <G> <N> : "Ν" U039D # GREEK CAPITAL LETTER NU
<Multi_key> <G> <P> : "Π" U03A0 # GREEK CAPITAL LETTER PI
<Multi_key> <G> <R> : "Ρ" U03A1 # GREEK CAPITAL LETTER RHO
<Multi_key> <G> <S> : "Σ" U03A3 # GREEK CAPITAL LETTER SIGMA
<Multi_key> <G> <T> : "Τ" U03A4 # GREEK CAPITAL LETTER TAU
<Multi_key> <G> <U> : "Υ" U03A5 # GREEK CAPITAL LETTER UPSILON
<Multi_key> <G> <F> : "Φ" U03A6 # GREEK CAPITAL LETTER PHI
<Multi_key> <G> <X> : "Χ" U03A7 # GREEK CAPITAL LETTER CHI
<Multi_key> <G> <O> : "Ω" U03A9 # GREEK CAPITAL LETTER OMEGA

# DOUBLES (additional stroke <Q>)
<Multi_key> <G> <Q> <T> : "Θ" U0398 # GREEK CAPITAL LETTER THETA
<Multi_key> <G> <Q> <O> : "Ο" U039F # GREEK CAPITAL LETTER OMICRON
<Multi_key> <G> <Q> <X> : "Ξ" U039E # GREEK CAPITAL LETTER XI
<Multi_key> <G> <Q> <P> : "Ψ" U03A8 # GREEK CAPITAL LETTER PSI

# greek small letters
<Multi_key> <g> <a> : "α" U03B1 # GREEK SMALL LETTER ALPHA
<Multi_key> <g> <b> : "β" U03B2 # GREEK SMALL LETTER BETA
<Multi_key> <g> <g> : "γ" U03B3 # GREEK SMALL LETTER GAMMA
<Multi_key> <g> <d> : "δ" U03B4 # GREEK SMALL LETTER DELTA
<Multi_key> <g> <e> : "ε" U03B5 # GREEK SMALL LETTER EPSILON
<Multi_key> <g> <z> : "ζ" U03B6 # GREEK SMALL LETTER ZETA
<Multi_key> <g> <h> : "η" U03B7 # GREEK SMALL LETTER ETA
<Multi_key> <g> <i> : "ι" U03B9 # GREEK SMALL LETTER IOTA
<Multi_key> <g> <k> : "κ" U03BA # GREEK SMALL LETTER KAPPA
<Multi_key> <g> <l> : "λ" U03BB # GREEK SMALL LETTER LAMDA
<Multi_key> <g> <m> : "μ" U03BC # GREEK SMALL LETTER MU
<Multi_key> <g> <n> : "ν" U03BD # GREEK SMALL LETTER NU
<Multi_key> <g> <p> : "π" U03C0 # GREEK SMALL LETTER PI
<Multi_key> <g> <r> : "ρ" U03C1 # GREEK SMALL LETTER RHO
<Multi_key> <g> <s> : "σ" U03C3 # GREEK SMALL LETTER SIGMA
<Multi_key> <g> <t> : "τ" U03C4 # GREEK SMALL LETTER TAU
<Multi_key> <g> <u> : "υ" U03C5 # GREEK SMALL LETTER UPSILON
<Multi_key> <g> <f> : "φ" U03C6 # GREEK SMALL LETTER PHI
<Multi_key> <g> <x> : "χ" U03C7 # GREEK SMALL LETTER CHI
<Multi_key> <g> <o> : "ω" U03C9 # GREEK SMALL LETTER OMEGA

# doubles (additional stroke <q>)
<Multi_key> <g> <q> <t> : "θ" U03B8 # GREEK SMALL LETTER THETA
<Multi_key> <g> <q> <o> : "ο" U03BF # GREEK SMALL LETTER OMICRON
<Multi_key> <g> <q> <p> : "ψ" U03C8 # GREEK SMALL LETTER PSI
<Multi_key> <g> <q> <s> : "ς" U03C2 # GREEK SMALL LETTER FINAL SIGMA
<Multi_key> <g> <q> <x> : "ξ" U03BE # GREEK SMALL LETTER XI

# prime etc
<Multi_key> <0> <apostrophe> : "′" U2032 # prime
<Multi_key> <0> <quotedbl> : "″" U2033 # double prime