Using gnome-software for Software Manager entry, using it icon too.

usr/lib/linuxmint/mintwelcome/mintwelcome.py

@@ -80,7 +80,7 @@ class MintWelcome():
         builder.get_object("button_codecs").connect("clicked", self.visit, "apt://mint-meta-codecs?refresh=yes")
         builder.get_object("button_new_features").connect("clicked", self.visit, new_features)
         builder.get_object("button_release_notes").connect("clicked", self.visit, release_notes)
-        builder.get_object("button_mintinstall").connect("clicked", self.launch, "synaptic")
+        builder.get_object("button_mintinstall").connect("clicked", self.launch, "gnome-software")
         builder.get_object("button_timeshift").connect("clicked", self.pkexec, "timeshift-gtk")
         builder.get_object("button_mintdrivers").connect("clicked", self.pkexec, "driver-manager")
         builder.get_object("button_gufw").connect("clicked", self.launch, "gufw")

usr/share/linuxmint/mintwelcome/mintwelcome.ui

@@ -1253,7 +1253,7 @@
                             <property name="visible">True</property>
                             <property name="can_focus">False</property>
                             <property name="halign">center</property>
-                            <property name="icon_name">software-properties</property>
+                            <property name="icon_name">org.gnome.Software</property>
                             <property name="icon_size">6</property>
                           </object>
                           <packing>
@@ -1296,7 +1296,7 @@
                           <object class="GtkLabel">
                             <property name="visible">True</property>
                             <property name="can_focus">False</property>
-                            <property name="label" translatable="yes">There are about 60,000 applications available. Linux Mint comes with the bare minimum to get you started. The Software Manager is there if you're looking for more.</property>
+                            <property name="label" translatable="yes">There are a lot of applications available, FUSS comes with the bare minimum to get you started. The Software Manager is there if you're looking for more.</property>
                             <property name="wrap">True</property>
                             <property name="xalign">0</property>
                           </object>