What you have described is the pure moment of input costs lowering (and you're confusing surplus value with price, 50 being surplus would also imply 10 in variable and 10 in constant, so 70 would be the input for company 2 if you simplify for the sake of example absolutely no tool usage in company 2). However, unless company 2 has a pure monopoly on chairs, this lowering of cost of production would also apply to other chair companies, and costs would lower. When wood prices are low, wooden chairs cost less than when wood prices are higher.

Further, the TRPF isn't really about competition, or even surplus value. That's one-sided. The TRPF is about rising organic composition of Capital, ie as c increases in ratio with v, or c/v. Competition pushes for this, as increasing automation can allow temporary advantage (as you've somewhat shown) before other companies follow suit. What you've shown is one company lowering the ratio of c/v, ie lowering the costs of their constant Capital over their variable, but that would imply that this company should never reduce wages nor increase automation as a rule.

In order to outcompete, constant Capital must rise in ratio, as it can lower prices of production below what others can offer, even though this raises c/v. Hence total profits rise, but rates of profit trend downwards.

Your argument would only hold true if this was the final part of the process and competition didn't exist for company 2, allowing them to charge monopoly prices and never worry about increasing automation and productivity.

Now, the rate of profit falling is often wholly combatted by increasing exploitation, or e=s/v. This, however, gives rise to stagnating real wages while the Capitalists get ever wealthier, sharpening class contradictions.