This means that it was compiled with pure-GTK (Wayland). You are seeing this warning as you are using X instead. I am not aware of another ppa, but there probably is one.
You could use the 'latest/edge' version of the snap instead:
sudo snap install emacs --edge --classic
Or even better imo just compile it yourself which is actually very easy and quite fast:
# Install dependencies for Ubuntu 22.04
# In older releases of Ubuntu some dependencies have other names or are not
# available. If you have Ubuntu 21.04 or an older release make sure to install
# tree-sitter from source to get native tree-sitter support.
# Got the dependencies from the snap and from 'apt-cache depends emacs-gtk'.
sudo apt install -y autoconf automake bsd-mailx dbus-x11 debhelper dpkg-dev \
gcc-10 libacl1-dev libasound2-dev libdbus-1-dev libgccjit-10-dev \
libgif-dev libgnutls28-dev libgpm-dev libgtk-3-dev libjansson-dev \
libjpeg-dev liblcms2-dev liblockfile-dev libm17n-dev libncurses5-dev \
liboss4-salsa2 libotf-dev libpng-dev librsvg2-dev libselinux1-dev \
libsystemd-dev libtiff-dev libxi-dev libxml2-dev libxpm-dev libxt-dev \
procps quilt sharutils texinfo zlib1g-dev gvfs language-pack-en-base \
libasound2 libaspell15 libasyncns0 libatk-bridge2.0-0 libatk1.0-0 \
libatspi2.0-0 libbrotli1 libc6 libc6-dev libcairo-gobject2 libcairo2 \
libcanberra-gtk3-0 libcanberra-gtk3-module libcanberra0 libdatrie1 \
libdb5.3 libdrm2 libegl1 libepoxy0 libflac8 libfontconfig1 libfreetype6 \
libgbm1 libgccjit0 libgcc-s1 libgdk-pixbuf2.0-0 libgif7 libgl1 \
libglvnd0 libglx0 libgpm2 libgraphite2-3 libgstreamer-gl1.0-0 \
libgstreamer-plugins-base1.0-0 libgstreamer1.0-0 libgtk-3-0 \
libgudev-1.0-0 libharfbuzz-icu0 libharfbuzz0b libhyphen0 libice6 \
libicu70 libisl23 libjansson4 libjbig0 libjpeg-turbo8 liblcms2-2 \
liblockfile1 libltdl7 libm17n-0 libmpc3 libmpfr6 libnotify4 libnss-mdns \
libnss-myhostname libnss-systemd libogg0 liborc-0.4-0 libotf1 \
libpango-1.0-0 libpangocairo-1.0-0 libpangoft2-1.0-0 libpixman-1-0 \
libpng16-16 libpulse0 librsvg2-2 libsasl2-2 libsecret-1-0 libsm6 \
libsndfile1 libsoup2.4-1 libssl3 libstdc++6 libtdb1 libthai0 libtiff5 \
libvorbis0a libvorbisenc2 libvorbisfile3 libwayland-client0 \
libwayland-cursor0 libwayland-egl1 libwayland-server0 libwebp7 \
libwebpdemux2 libwoff1 libx11-6 libx11-xcb1 libxau6 libxcb-render0 \
libxcb-shm0 libxcb1 libxcomposite1 libxcursor1 libxdamage1 libxdmcp6 \
libxext6 libxfixes3 libxi6 libxinerama1 libxkbcommon0 libxml2 libxpm4 \
libxrandr2 libxrender1 libxslt1.1 libyajl2 libwebp-dev libtree-sitter0 \
libtree-sitter-dev emacs-bin-common emacs-common libcairo2-dev \
libdbus-1-3 libfontconfig1-dev libfreetype6-dev libglib2.0-0 libgmp10 \
libgnutls30 libgpm2 libharfbuzz0b libjpeg8-dev libtinfo-dev \
build-essential libxfixes-dev libxrender-dev libsqlite3-dev libc6 \
libc6-dev libenchant-2-dev
# Clone Emacs master
cd ~
git clone --depth 1 git://git.sv.gnu.org/emacs.git
# Install it
export CC="gcc-10" CXX="gcc-10"
./autogen.sh
# Turns native compilation on. Remove if you don't want this.
./configure --with-json --with-native-compilation
make -j $(nproc)
sudo make install