Failed to load Steamui.dll error

In most cases it's practical to start troubleshooting a malfunctioning program by running it as an administrator of your system.
This is likely not the cause here, but it can help speeding up the process.

Temporarily disable any third-party firewall, anti-virus software (Windows Defender usually plays nice, for a change), or other intrusive software, and try restarting Steam.
Take caution, as this will also temporarily leave your system vulnerable, so be sure to re-enable directly after a problem is fixed (that is: disable only during that window of restarting Steam).

Try deleting that Libswscale-4.dll file: it surely is a newer version of Libswscale-3.dll, and, in any case, if Steam is missing files, it will redownload them.

There are a few more fixes explicitly for your case mentioned in this Steam Community thread, most successful of which seem to be (or seems to be a combination of) the following steps [edited slightly for readability]:

All you have to do is restart your computer in Safe Mode. Delete all of your Steam files other than the AppData folder and the Steam.exe file. Double click Steam.exe and it should successfully install the update.

and

Fastest way, instead of redownloading after deleting the files in Safe Mode, is to add the following parameters to your Steam shortcut: -clientbeta client_candidate (e.g. "C:Program FilesSteamSteam.exe" -clientbeta client_candidate).

Now, before you try this in Safe Mode, I suggest deleting the mentioned files - as administrator - in the normal Windows mode, creating a shortcut, adding those parameters, and running it - as administrator. If that doesn't work, you can always fiddle around in Safe Mode.