How to make an interactive solver function?

Question

I am working on creating a function that takes in any physics equation as a string and converts it to an equation that I will then paste into an interactive interface as asked here: How to make an interactive calculator for any mathematical relation?. I am implementing the first answer as a function that accepts any physics equation as a string and does two things before replacing the example of a^2+b^2==c^2.

First I want to replace any instance of "=" with "==" except for an instance of "==". The goal of this is to make a user-friendly function if the user enters an equation with incorrect programming syntax. I will then convert it to an expression.

Second, after it has been converted to an expression I will extract the symbols from the equation using this code, which I got from How to find all symbols in an expression and perform an operation on them?.

Symbols[x_String] := 
 DeleteDuplicates@Cases[ToExpression[x], _Symbol, Infinity]

The function for the first program is as follows:

StringReplace["\!\(\*SuperscriptBox[\(a\), \
\(2\)]\)+\!\(\*SuperscriptBox[\(b\), \
\(2\)]\)==\!\(\*SuperscriptBox[\(c\), \(2\)]\)", 
 Except[{"=="}, "="] -> "=="]

I am trying to base my code off this example

StringReplace["the cat in the hat", 
 Except[Characters["aeiou"], "c"] -> ""]

Unfortunately, this causes an error: I am not sure what I am doing wrong here.

EDIT: I have my attempt here: https://www.wolframcloud.com/obj/burbery1/Published/Interactive%20Solver%20Function.nb In the process I came across two more unexpected hurdles: if the variable the user is solving for was already defined in a previous call of Interactive Solver or another piece of program that already executed, the symbol is regarded as a numerical value and not a variable.

The second problem is that the InteractiveSolver function returns a list of Null values when I run it for some reason.

I tried some code provided as an answer to this question and encountered the following error:

Answer 1

FWIW, my take on the big problem. I'm not particularly interested in parsing strings, so I can delete if this is unhelpful.

(*"
 *  Calculator
"*)
CellPrint@
 ExpressionCell[
  Manipulate[
   Column[{
     (* displays some data for inspection *)
     Dynamic@{var, formula},
     Dynamic@Quiet[
       (* TBD:check input/output of Solve *)
       With[{sol = Solve[ReleaseHold@formula, var]},
        With[{sol0 = 
           sol /. Thread[freevariables -> value /@ freevariables]},
         value[var] = var /. Last[sol0];(* last sol *)
         Grid@Transpose@{sol, sol0} /. Rule -> Equal
         ]],
       {Power::infy}],
     (* parameter inputs *)
     Grid@Transpose@{
        freevariables,
        InputField[Dynamic@value@#] & /@ freevariables}
     }],
   
   {{formula, formula}, (* user input = held expression *)
    InputField[Dynamic[formula,
       ({formula, variables, var} = parseFormula[#];
         Clear[value];
         (value[#] = 1) & /@ variables;
         freevariables = DeleteCases[variables, var];
         ) &],
      Hold@Expression] &},
   {{var, var}, Dynamic@variables, SetterBar, TrackingFunction -> (
      (var = #;
        freevariables = DeleteCases[variables, var]) &)},
   {{variables, variables}, None},
   {{freevariables, freevariables}, None},
   {{parseFormula, parseFormula}, None},
   {{value, value}, None},(* stores values of parameters *)
   
   Initialization :> (
     (* utility (parses held expression) *)
     parseFormula // ClearAll;
     parseFormula[f_] := Module[{myformula, myvars, myvar},
       myformula = 
        f /. {Set | SetDelayed | Rule | RuleDelayed -> Equal,
          Null -> $Failed}; (* TBD: Handle user error *)
       myvars = Reduce`FreeVariables[ReleaseHold@myformula];
       myvar = Replace[{myformula, myvars},
         {{Hold[v_ == _] /; MemberQ[myvars, v], _} :> v,
          {_, {a_, ___}} :> a,
          {_, v_} :> v (* TBD: Handle user error *)
          }];
       myformula = Replace[myformula,
         {eq : Hold[_Equal] :> eq,
          Hold[x_] /; Internal`WouldBeNumericQ[x, Evaluate@myvars] :>
           (myvar = $ans; 
            PrependTo[myvars, $ans];
            Hold[$ans == x]),
          form_ :> (myvars = myvar = $Failed; form)
          }]; (* TBD: Handle user error *)
       {myformula, myvars, myvar}
       ];
     (* init *)
     {formula, variables, var} = 
      parseFormula[ToExpression["a^2+b^2==c^2", StandardForm, Hold]];
     freevariables = DeleteCases[variables, var];
     (value[#] = 1) & /@ variables;
     )
   ],
  "Output",
  CellContext -> Cell]