Anyone else getting this error? I checked my package manager and I have libssl3 (32 and 64 bit) installed. I am on Mint 21.

EDIT: Found it myself, guess I'll just leave the topic up. libssl1.1 is required right now.
See https://forums.stardewvalley.net/threads/no-supported-version-of-libssl-was-found-ubuntu-22-04.12155/

Same here, right after downloading and installing on Arch Linux. I have openssl installed with what I believe has the needed files.

$ ./start.sh
Running Stardew Valley
./StardewValley: line 7: sw_vers: command not found
NoFpsCap: This feature is not available
setGameMode( 'titleScreenGameMode (0)' )
loadPreferences(); begin - languageCode=
No usable version of libssl was found
./StardewValley: line 27: 75959 Aborted (core dumped) ./"Stardew Valley" $@

$ sudo pacman -Qi openssl
Name : openssl
Version : 3.0.7-4
Description : The Open Source toolkit for Secure Sockets Layer and Transport Layer Security
Architecture : x86_64
URL : www.openssl.org
Licenses : Apache
Groups : None
Provides : libcrypto.so=3-64 libssl.so=3-64
Depends On : glibc
Optional Deps : ca-certificates [installed]
perl [installed]
Required By : coreutils cryptsetup curl git gst-plugins-bad kmod ldns lib32-openssl libarchive libevent libgit2
libsasl libshout libssh libssh2 libtorrent-rasterbar nodejs openssh openvpn opusfile ostree
pkcs11-helper python srt sudo systemd tpm2-tss vpnc wpa_supplicant xmlsec
Optional For : None
Conflicts With : None
Replaces : openssl-perl openssl-doc
Installed Size : 10.69 MiB
Packager : Pierre Schmitz <pierre@archlinux.org>
Build Date : Wed 14 Dec 2022 09:22:44 AM PST
Install Date : Wed 21 Dec 2022 09:53:24 PM PST
Install Reason : Installed as a dependency for another package
Install Script : No
Validated By : Signature

I fixed it on Arch Linux. Just needed to install package openssl-1.1 and now the game loads.

sudo pacman -S openssl-1.1

hope this helps those on Arch.