refactor: rewrite connection expansion implementation #2837
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                          Spell Check with Typos: 
                        ./src/systems/problem_utils.jl#L1637
                      
                       
                  "appent" should be "append". 
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                          Spell Check with Typos: 
                        ./src/systems/system.jl#L1075
                      
                       
                  "indepent" should be "independent". 
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                          Spell Check with Typos: 
                        ./src/structural_transformation/symbolics_tearing.jl#L936
                      
                       
                  "varible" should be "variable". 
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                          Spell Check with Typos: 
                        ./src/modelingtoolkitize/common.jl#L290
                      
                       
                  "proble" should be "probe" or "probably" or "problem". 
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                          Spell Check with Typos: 
                        ./src/modelingtoolkitize/common.jl#L49
                      
                       
                  "proble" should be "probe" or "probably" or "problem". 
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